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Quizzes > High School Quizzes > Mathematics

8th Grade Functions Practice Quiz

Master 8th Grade Transformations With Engaging Practice

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting a Transformations and Functions Challenge quiz for high school math students.

Which transformation results in shifting the graph of y = f(x) upward by 4 units?
y = f(x) - 4
y = f(x) + 4
y = f(x - 4)
y = f(x) / 4
Adding 4 to the function f(x) increases every output value by 4, which shifts the entire graph upward. This is the standard vertical translation of a function.
What does the transformation y = f(x - 3) do to the graph of a function?
Shifts the graph to the right by 3 units
Shifts the graph to the left by 3 units
Shifts the graph downward by 3 units
Shifts the graph upward by 3 units
In the transformation y = f(x - 3), the subtraction inside the argument causes the graph to move to the right by 3 units. This is a basic horizontal translation rule for functions.
What effect does multiplying the function f(x) by -1, as in y = -f(x), have on its graph?
It compresses the graph horizontally
It reflects the graph across the x-axis
It reflects the graph across the y-axis
It stretches the graph vertically
Multiplying f(x) by -1 changes the sign of every output value, reflecting the graph over the x-axis. This is a common reflection transformation in function analysis.
In the transformation y = 2f(x), what happens to the graph of the function?
It is vertically compressed by a factor of 2
It is vertically stretched by a factor of 2
It is shifted upward by 2 units
It is horizontally stretched by a factor of 2
Multiplying f(x) by 2 amplifies all y-values, stretching the graph vertically by a factor of 2. The width of the graph remains unchanged.
What is the effect of the transformation y = f(2x) on the graph of y = f(x)?
A horizontal compression by a factor of 1/2
A vertical stretch by a factor of 2
A horizontal stretch by a factor of 2
A vertical compression by a factor of 1/2
Replacing x with 2x means the input values must be halved to achieve the same output, resulting in a horizontal compression by a factor of 1/2. This does not affect the vertical dimension.
Consider the transformation y = -3f(x + 2) - 4. Which sequence of transformations is applied to the graph of f(x)?
Shift left by 2, vertical stretch by 3, reflect across the x-axis, then shift down by 4
Shift left by 2, horizontal compression by 3, reflect across the x-axis, then shift up by 4
Shift right by 2, horizontal stretch by 3, reflect across the y-axis, then shift up by 4
Shift right by 2, vertical compression by 3, reflect across the x-axis, then shift down by 4
The term f(x + 2) shifts the graph left by 2 units, while multiplying by -3 reflects it over the x-axis and stretches it vertically by 3. Finally, subtracting 4 shifts the graph downward by 4 units.
If g(x) = f(x) + 5 and h(x) = f(x + 5), which transformation represents a vertical shift?
g(x) represents a vertical shift upward by 5
h(x) represents a horizontal shift left by 5
h(x) represents a vertical shift upward by 5
g(x) represents a horizontal shift left by 5
Adding 5 to f(x) as in g(x) = f(x) + 5 moves every output value up by 5 units, which is a vertical shift. In contrast, modifying the input as in h(x) changes the horizontal position.
Which transformation results in a horizontal stretch of the graph of f(x) by a factor of 3?
y = f(3x)
y = f(x/3)
y = 3f(x)
y = f(x) / 3
Dividing the input by 3, as in y = f(x/3), stretches the graph horizontally by a factor of 3. Multiplying the input by 3 would instead compress the graph.
What transformation does y = 1/2 f(-x) perform on the graph of f(x)?
Reflection across the x-axis and horizontal compression by a factor of 1/2
Vertical stretch by a factor of 1/2 and reflection across the x-axis
Reflection across the y-axis and vertical compression by a factor of 1/2
Horizontal stretch by a factor of 1/2 and reflection across the y-axis
The negative inside f(-x) reflects the graph over the y-axis, and the factor 1/2 outside compresses it vertically. This combination of operations produces the required transformation.
If a function f(x) has a point (2, 3) and it is transformed by y = f(2x - 2) + 1, what will be the coordinates of the corresponding point on the transformed graph?
(3, 1)
(2, 3)
(2, 4)
(1, 3)
To find the new x-coordinate, set 2x - 2 = 2, which gives x = 2. The new y-coordinate is obtained by adding 1 to the original y-value, so 3 + 1 = 4. Thus, the transformed point is (2, 4).
Which transformation reflects the graph of f(x) over the y-axis?
y = f(x) + f(-x)
y = f(-x)
y = f(x) - f(-x)
y = -f(x)
Replacing x with -x in f(x) produces the mirror image of the graph across the y-axis. This is the standard method to reflect a function horizontally.
What is the effect of the transformation y = -f(x + 1) on the original function f(x)?
It horizontally compresses the graph and shifts it down by 1 unit
It reflects the graph over the x-axis after shifting it left by 1 unit
It vertically stretches the graph and shifts it right by 1 unit
It reflects the graph over the y-axis after shifting it right by 1 unit
The transformation f(x + 1) shifts the graph left by 1 unit and the negative sign outside the function reflects it across the x-axis. This combined operation first translates and then reflects the graph.
For a function f(x), what does the transformation y = f(x) - 3 do to its graph?
Reflects the graph across the x-axis
Shifts the graph upward by 3 units
Horizontally compresses the graph
Shifts the graph downward by 3 units
Subtracting 3 from f(x) decreases each y-value by 3, which moves the graph downward by 3 units. There is no reflection or horizontal change involved in this transformation.
If a function transforms as y = 2f(0.5x - 4) + 7, what sequence of transformations does the graph of f(x) undergo?
Horizontal compression by a factor of 2, shift left by 8, vertical compression by a factor of 2, then shift down by 7
Horizontal stretch by a factor of 2, shift left by 8, vertical stretch by a factor of 2, then shift up by 7
Horizontal compression by a factor of 2, shift right by 8, vertical stretch by a factor of 2, then shift up by 7
Horizontal stretch by a factor of 2, shift right by 8, vertical stretch by a factor of 2, then shift up by 7
By rewriting 0.5x - 4 as 0.5(x - 8), we see that the graph is horizontally stretched by a factor of 2 and shifted right by 8 units. The multiplication by 2 outside stretches the graph vertically, and adding 7 shifts it upward.
Which transformation compresses the graph of f(x) vertically by a factor of 1/2?
y = (1/2)f(x)
y = f(x/2)
y = 2f(x)
y = f(1/2 x)
Multiplying f(x) by 1/2 reduces every output value by half, leading to a vertical compression by a factor of 1/2. Other forms affect horizontal dimensions or have the opposite effect.
Given the transformation y = -2f(3 - x) + 5, which sequence of transformations is applied to f(x)?
Reflect horizontally, shift right by 3 units, reflect vertically with a stretch factor of 2, then shift up by 5
Shift left by 3 units, stretch vertically by 2, then reflect horizontally and shift up by 5
Reflect vertically, shift left by 3 units, stretch horizontally by 2, then shift down by 5
Shift right by 3 units, reflect vertically, stretch horizontally by 2, then shift up by 5
Rewriting 3 - x as -(x - 3) reveals a horizontal reflection and a right shift by 3. The multiplier -2 produces a vertical reflection along with a vertical stretch by 2, and the +5 shifts the graph upward.
If a point (a, b) lies on the graph of y = f(x), what is its image under the transformation y = f(2x + 6) - 3?
((a - 6)/2, b + 3)
((a + 6)/2, b + 3)
((a - 6)/2, b - 3)
((2a - 6), b - 3)
To find the new x-coordinate, set 2x + 6 = a, yielding x = (a - 6)/2. The y-coordinate is adjusted by subtracting 3 from b. This results in the point ((a - 6)/2, b - 3).
Which transformation is equivalent to y = f((x + 4)/2)?
A horizontal stretch by a factor of 2 followed by a shift left by 4 units
A vertical stretch by a factor of 2 followed by a shift left by 4 units
A horizontal stretch by a factor of 2 followed by a shift right by 4 units
A horizontal compression by a factor of 2 followed by a shift right by 4 units
Expressing (x + 4)/2 shows that the x-values are first stretched by a factor of 2; the addition inside the argument indicates a shift left by 4 units. This combination is accurately described in option A.
The transformation y = 3 - f(1 - x) involves which of the following operations on f(x)?
A vertical stretch followed by a horizontal shift to the right and a downward shift of 3
A horizontal reflection (with a shift) and a vertical reflection with an upward shift of 3
A horizontal reflection (without shift) and a vertical stretch with an upward shift of 3
A horizontal compression and a vertical reflection with a downward shift of 3
Rewriting 1 - x as -(x - 1) reveals a horizontal reflection combined with a right shift by 1 unit. The negative sign in front of the function and the addition of 3 indicate a vertical reflection and an upward translation of 3 units.
Which composite transformation maps the graph of y = f(x) to y = -1/2 f(-2x + 4) - 3?
Reflect vertically, horizontally compress by factor 2, then shift right by 2 units and shift down by 3
Reflect horizontally and vertically, horizontally compress by factor 1/2, vertically compress by factor 1/2, shift right by 2 units, then shift down by 3
Reflect horizontally, horizontally compress by factor 1/2, reflect vertically, vertically compress by factor 1/2, shift left by 2 units, then shift up by 3
Reflect horizontally, horizontally stretch by factor 2, reflect vertically, vertically stretch by factor 2, shift left by 2 units, then shift up by 3
By rewriting -2x + 4 as -2(x - 2), we identify a horizontal reflection with a compression by factor 1/2 and a right shift of 2 units. The multiplier -1/2 outside applies a vertical reflection and compression, and subtracting 3 shifts the graph downward.
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Study Outcomes

  1. Understand the effects of horizontal and vertical shifts on function graphs.
  2. Analyze how reflections, stretches, and compressions alter function behavior.
  3. Apply transformation concepts to graph functions from algebraic equations.
  4. Synthesize multiple transformations to interpret complex function scenarios.

8th Grade Functions & Transformations Cheat Sheet

  1. Understand Vertical and Horizontal Shifts - Turning graphs into acrobats is easier than you think! Adding +k to f(x) lifts it up by k units, while f(x − h) scoots it right by h units (or left if h is negative). Mastering these moves lets you place any curve exactly where you want it. Learn more
  2. Master Reflections Over Axes - Ready to see your graph take a mirror selfie? Multiply by −1 to flip over the x-axis, or swap x with −x for a y-axis reversal. It's like giving your function a front”flip or back”flip - super satisfying to get right! Flip it with a click
  3. Learn Vertical and Horizontal Scaling - Stretch your curve sky-high by multiplying by a factor >1, or squash it toward the x-axis with a fraction between 0 and 1. Swap x for x/c to squeeze it sideways, or cx to pull it wide. Think of it as giving your graph a workout or a cozy hug. Scale like a pro
  4. Combine Multiple Transformations - Why stop at one trick when you can juggle three? Always remember order: reflect and scale first, then translate. For example, −f(x)+3 flips the graph and then raises it by 3 units - voilà, a perfect combo move! Try combos here
  5. Practice with Interactive Tools - Nothing beats hands-on play! GeoGebra lets you drag, drop and tweak graphs in real time, so you see instant feedback on your transformations. It's like a sandbox for functions - endless fun and learning. Explore GeoGebra
  6. Recognize Parent Functions - Every graph transformation starts with a familiar friend: the parent function. Whether it's linear, quadratic or absolute value, knowing the base shape makes all the shifts and stretches a breeze. Memorize these, and you'll decode any transformed graph in seconds. Meet the parents
  7. Apply Transformations to Real-World Problems - Graphs aren't just for exams - they model everything from roller coasters to population trends. Practice fitting curves to data and predicting outcomes by tweaking transformations. It's math with real impact! Solve real-world examples
  8. Understand the Order of Transformations - Sequence matters: reflect & scale first, then shift - otherwise you'll end up chasing your own tail. This "RST" routine (Reflect, Stretch, Translate) keeps your workflow smooth and error-free. Nail this order, and complex transformations feel like shooting fish in a barrel. Get the order down
  9. Use Mnemonics to Remember Transformations - When your brain feels foggy, a catchy phrase can save the day. Try "Reflect, Stretch, Translate" or invent your own rhyme - just keep it short and silly. Mnemonics turn rote steps into memorable jams! Find your rhyme
  10. Practice with Diverse Functions - Once you've got the basics, tackle polynomials, exponentials and trig graphs to level up. Each function type brings its own quirks, so variety keeps your skills sharp. The more you practice, the more confident you'll become. Challenge yourself
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