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Quizzes > High School Quizzes > Electives

Unit 3: Parent Functions & Transformations Quiz

Master Graphing Skills and Function Transformations Now

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art illustrating a trivia quiz on Transforming Parent Functions for high school algebra students.

What is the resulting function when f(x) = x² is translated 3 units upward?
x² + 3
-x² + 3
-x² - 3
x² - 3
Translating a function upward by 3 units adds 3 to the output. Therefore, the new function is x² + 3.
Which function represents the graph of f(x) = |x| after a reflection over the x-axis?
-x
-|x|
|-x|
|x|
Reflecting over the x-axis multiplies the output by -1, resulting in -|x|. The other options do not correctly apply the reflection.
How is the graph of f(x) = √x shifted when it is translated 4 units to the right?
√(x - 4)
√(x + 4)
√x - 4
4√x
A horizontal shift to the right is accomplished by replacing x with (x - 4), yielding √(x - 4).
What is the effect of a vertical stretch by a factor of 2 on the function f(x) = 1/x?
2/x
1/(2x)
x - 2
x/2
Multiplying the function by 2 results in 2/x, which stretches the graph vertically by a factor of 2.
After translating f(x) = x two units to the left, what is the new function?
-x - 2
-x + 2
x + 2
x - 2
A horizontal translation left by 2 is achieved by replacing x with (x + 2), resulting in x + 2.
Which function represents the transformation of f(x) = √x after a reflection over the y-axis followed by a horizontal shift 2 units to the right?
√(-x - 2)
√(2 - x)
√(x - 2)
√(x + 2)
Reflecting the function √x over the y-axis yields √(-x), and shifting it 2 units to the right replaces x with (x - 2), resulting in √(2 - x).
For the function f(x) = x², what is the resulting function after a horizontal compression by a factor of 1/2 and a vertical stretch by a factor of 3?
(1/12)x²
(3/4)x²
12x²
3x²
A horizontal compression by 1/2 replaces x with 2x, so (2x)² becomes 4x². Multiplying by 3 yields 12x².
Which transformation applied to f(x) = 1/x results in a vertical asymptote at x = -1 and a horizontal asymptote at y = 2?
2/(x-1) + 1
2/(x+1) + 1
1/(x+1) + 2
1/(x-1) + 2
Replacing x with (x+1) shifts the vertical asymptote to x = -1, and adding 2 shifts the horizontal asymptote to y = 2.
If f(x) = x² is first reflected over the x-axis and then translated 4 units to the left, which function represents this transformation?
-(x+4)²
-(x-4)²
x² - 4
(x+4)²
Reflecting f(x) = x² over the x-axis gives -x², and translating it left by 4 replaces x with (x+4), resulting in -(x+4)².
Given f(x) = √x, find the function after a vertical compression by a factor of 1/2 and a 3-unit downward shift.
√(x/2) - 3
(1/2)√x - 3
√x - 3/2
(1/2)√(x-3)
Multiplying √x by 1/2 compresses it vertically, and subtracting 3 shifts it downward, resulting in (1/2)√x - 3.
What is the inverse of f(x) = x³, obtained by reflecting its graph across the line y = x?
∛x
x³
1/x³
-x³
Reflecting the graph of f(x) = x³ over the line y = x yields its inverse, which is the cube root function ∛x.
If f(x) = √x is translated 5 units to the left and then reflected over the y-axis, which function represents the resulting graph?
-√(x+5)
√(x - 5)
√(x+5)
√(5 - x)
Translating left 5 units gives √(x+5), and reflecting over the y-axis replaces x with -x, resulting in √(5 - x).
The graph of f(x) = 1/(x-2) represents which transformation of the parent function f(x) = 1/x?
A reflection over the y-axis
A horizontal stretch by a factor of 2
A horizontal shift 2 units to the right
A vertical shift 2 units upward
Replacing x with (x-2) shifts the vertical asymptote from x = 0 to x = 2, which is a horizontal shift to the right.
What is the effect of a vertical stretch by a factor of 4 on the parent function f(x) = |x|?
|x|/4
|x| + 4
4|x|
|4x|
A vertical stretch multiplies the entire function by the factor, so |x| becomes 4|x|.
Determine the transformation applied to f(x) = √(x+1) when it is horizontally stretched by a factor of 2.
√(x+2)
(1/2)√(x+1)
√(x/2 + 1)
√(2x+1)
Horizontal stretching by a factor of 2 involves replacing x with x/2. Thus, √(x+1) becomes √((x/2)+1).
For f(x) = x², what transformations are applied in the function g(x) = -3*(x-2)² + 5?
A horizontal shift right 2, a vertical stretch by 3, a reflection over the x-axis, and a vertical shift upward 5
A horizontal shift left 2, a vertical compression by 3, a reflection over the y-axis, and a vertical shift downward 5
A horizontal shift right 2, a vertical stretch by 3, and a vertical shift upward 5 without reflection
A horizontal shift right 2, a vertical compression by 3, a reflection over the x-axis, and a vertical shift upward 5
g(x) = -3*(x-2)² + 5 is obtained by shifting x² right by 2, reflecting it over the x-axis (due to the negative sign), vertically stretching it by 3, and then shifting it upward by 5.
Find the sequence of transformations that converts f(x) = 1/x into h(x) = -2/(x+4) + 3.
A horizontal shift left by 4, a vertical stretch by 2, a reflection over the x-axis, followed by a vertical shift upward 3
A horizontal shift right by 4, a vertical stretch by 2, a reflection over the y-axis, and a vertical shift downward 3
A horizontal shift left by 4, a vertical stretch by 2, a reflection over the y-axis, and a vertical shift upward 3
A horizontal shift left by 4, a vertical compression by 2, a reflection over the x-axis, and a vertical shift upward 3
Starting with f(x) = 1/x, replacing x with (x+4) shifts the graph left by 4. Multiplying by -2 creates a vertical stretch and reflection over the x-axis, and adding 3 shifts the graph upward.
How does the graph of f(x) = x² change when it is transformed into g(x) = (1/2)(-(x+3)²) - 4?
It is shifted right by 3, reflected over the y-axis, vertically stretched by a factor of 2, and moved up 4 units
It is shifted left by 3, reflected over the x-axis, vertically stretched by a factor of 1/2, and moved down 4 units
It is shifted left by 3, reflected over the x-axis, vertically compressed by a factor of 1/2, and moved down 4 units
It is shifted left by 3 with a vertical compression by 1/2 and a downward shift of 4 units, with no reflection
The transformation g(x) applies a horizontal shift left by 3 (x+3), a reflection over the x-axis (negative sign), a vertical compression by multiplying by 1/2, and a downward shift subtracting 4.
Which function results from applying a reflection over the x-axis followed by a horizontal compression by a factor of 1/2 to f(x) = √x?
-√(x/2)
-√(2x)
√(2x)
√(x/2)
Reflecting f(x) = √x over the x-axis gives -√x, and a horizontal compression by a factor of 1/2 means replacing x with 2x, which yields -√(2x).
In converting f(x) = |x| into g(x) = 3|x+2| - 1, what is the correct order of transformations?
A vertical shift downward by 1, a horizontal shift left by 2, then a vertical stretch by 3
A vertical stretch by 3, a horizontal shift left by 2, then a vertical shift downward by 1
A horizontal shift left by 2, a vertical shift downward by 1, then a vertical stretch by 3
A horizontal shift left by 2, a vertical stretch by 3, then a vertical shift downward by 1
The function g(x) = 3|x+2| - 1 is obtained by first shifting |x| left by 2, then stretching it vertically by a factor of 3, and finally shifting it downward by 1.
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Study Outcomes

  1. Analyze how translations, reflections, stretches, and compressions alter the graph of a parent function.
  2. Apply transformation techniques to rewrite parent functions in modified algebraic forms.
  3. Interpret shifts and changes in function behavior based on graphical transformations.
  4. Compare and contrast the effects of various transformation types on function graphs.
  5. Synthesize multiple transformations to generate complex function graphs for problem-solving.

Parent Functions & Transformations Cheat Sheet

  1. Master vertical and horizontal shifts - Shifting is as easy as adding constants: adding a number outside f(x) pushes the graph up or down, while tweaking the x inside f(x) slides it left or right. Think of it like dragging your favorite sticky note across the whiteboard without changing its shape. 3.5 Transformation of Functions - Algebra and Trigonometry | OpenStax
  2. Reflect functions over the axes - When you multiply the whole function by -1, it's like flipping your graph upside down over the x-axis; replace x with -x and you mirror it over the y-axis. Reflection gives you a brand-new perspective without altering the curve's steepness. 3.5 Transformation of Functions - College Algebra with Corequisite Support | OpenStax
  3. Explore vertical stretches and compressions - Scaling f(x) by a number greater than 1 stretches it away from the x-axis like pulling on a rubber band, while factors between 0 and 1 squash it closer. This tweak changes the "height" of peaks and valleys without shifting them sideways. Transformations of Functions Refresher - MathBitsNotebook(A2)
  4. Learn horizontal stretches and compressions - Multiply the inside x by a factor greater than 1 to compress the graph toward the y-axis, or by a fraction to stretch it out wider. It's like editing a photo's width: big numbers shrink it, small ones expand it sideways. Transformations of Functions - MathBitsNotebook(A2)
  5. Combine multiple transformations - Layer shifts, flips, and scales in any order to create wild new versions of your original graph. Like stacking filters on an Instagram photo, each step modifies the last, so the sequence you apply them really matters! 3.5 Transformation of Functions - College Algebra 2e | OpenStax
  6. Spot even and odd function symmetry - Even functions look the same on both sides of the y-axis like perfect butterflies, while odd ones spin around the origin after a 180° rotation. Recognizing these symmetries can save you tons of graphing time. 3.5 Transformation of Functions - College Algebra with Corequisite Support | OpenStax
  7. Practice reading transformations from equations - Spotting f(x − 2)+3 means a right-2 and up-3 move - like following a treasure map for graphs. The change inside x shifts horizontally, the outside change shifts vertically, making it easy once you see the pattern. Transformations of Functions - MathBitsNotebook(A2)
  8. Understand negative multipliers - A negative factor both flips and scales: its sign dictates the reflection over an axis, and its absolute value determines the stretch or squash. Think of it as a two-for-one transformation deal! Transformations of Functions Refresher - MathBitsNotebook(A2)
  9. Graph by transforming key points - Pick landmark points on your original curve, apply each transformation to them, and then connect the dots. This hands-on approach turns abstract algebra into a clear sketch you can draw by hand. 3.5 Transformation of Functions - Algebra and Trigonometry | OpenStax
  10. Use tech to verify your work - Don't be afraid to let Desmos or a graphing calculator double-check your moves! Seeing your predicted shifts, stretches, and flips pop up on-screen helps you catch mistakes and build confidence. 3.5 Transformation of Functions - College Algebra 2e | OpenStax
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