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Quizzes > High School Quizzes > Mathematics

Practice Quiz: Graph of the Function

Test your skills with clear graph explanations

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Function Graph Frenzy, a high school math quiz.

Which function has a graph that is a straight line?
f(x) = 2x + 3
f(x) = x^2
f(x) = sqrt(x)
f(x) = |x|
A straight line graph represents a linear function, typically in the form f(x) = mx + b. The function f(x)= 2x + 3 fits that form, while the others represent curves.
Which function produces a U-shaped graph?
f(x) = x
f(x) = -x^2
f(x) = x^2
f(x) = |x|
A U-shaped graph indicates a parabola opening upward. f(x)= x^2 is an upward-opening parabola, while f(x) = -x^2 would open downward.
Which function graph is V-shaped?
f(x) = 2x + 1
f(x) = x^3
f(x) = |x|
f(x) = x^2
A V-shaped graph is characteristic of absolute value functions. Among the options, f(x)= |x| clearly displays a V-shape.
Which option represents a horizontal shift of the function f(x) = x^2 to the right by 3 units?
f(x) = x^2 + 3
f(x) = (x-3)^2
f(x) = (x-3)^2 + 3
f(x) = (x+3)^2
A horizontal shift to the right by 3 units is achieved by replacing x with (x-3) in the function. Therefore, f(x) = (x-3)^2 is the correct transformation without any additional vertical shift.
Which function has a graph that is symmetric about the y-axis?
f(x) = x^3
f(x) = x^2
f(x) = x
f(x) = 2x + 1
A function is symmetric about the y-axis if it is even, meaning f(-x) equals f(x). The function f(x)= x^2 meets this criterion, while the others do not.
Which graph represents the function f(x)= -x^2 + 4?
A downward-opening parabola with vertex at (0,-4)
A downward-opening parabola with vertex at (0,4)
A straight line passing through (0,4)
An upward-opening parabola with vertex at (0,4)
The function f(x)= -x^2 + 4 is a parabola that opens downward because of the negative coefficient and its vertex is located at (0,4). The other options do not match these attributes.
Which graph shows the function f(x)= |x - 2|?
A U-shaped parabola with vertex at (2,0)
A V-shaped graph with vertex at (2,0)
A straight line crossing through (2,0)
A V-shaped graph with vertex at (-2,0)
The function f(x)= |x-2| shifts the standard absolute value graph so that its vertex is at (2,0). The other options either place the vertex incorrectly or describe a different graph shape.
Which function represents a vertical stretch of f(x)= x^2 by a factor of 3?
f(x)= 3x^2
f(x)= x^2 + 3
f(x)= x^2 - 3
f(x)= (x/3)^2
A vertical stretch multiplies all output values of the function by the given factor. Thus, f(x)= 3x^2 stretches the graph vertically by a factor of 3 compared to f(x)= x^2.
Which transformation represents reflecting the graph of f(x)= sqrt(x) over the x-axis?
f(x)= sqrt(-x)
f(x)= sqrt(x) (no reflection)
f(x)= -sqrt(x)
f(x)= -sqrt(-x)
Reflecting a graph over the x-axis involves multiplying the output by -1. Therefore, f(x)= -sqrt(x) correctly represents the reflection of f(x)= sqrt(x) over the x-axis.
For the function f(x)= 2|x| - 5, what is the vertex of its graph?
(-2, -5)
(0, 5)
(0, -5)
(2, -5)
In the function f(x)= 2|x| - 5, the graph's vertex occurs where the absolute value term is minimized (at x = 0), resulting in the point (0, -5). The other options do not match the transformation applied.
Which function graph represents a horizontal shift left by 4 units of f(x)= x^3?
f(x)= x^3 + 4
f(x)= (x+4)^3
f(x)= (x-4)^3
f(x)= x^3 - 4
A horizontal shift to the left by 4 units is achieved by replacing x with (x+4). Therefore, f(x)= (x+4)^3 is the correct transformation of f(x)= x^3.
Which function represents the reflection of f(x)= 2^x across the y-axis?
f(x)= -2^(-x)
f(x)= 2^x (no reflection)
f(x)= -2^x
f(x)= 2^(-x)
Reflecting a function across the y-axis involves replacing x with -x. Hence, f(x)= 2^(-x) is the reflection of f(x)= 2^x.
What is the effect on the graph of f(x)= ln(x) when it is shifted upward by 3 units?
f(x)= ln(x) + x
f(x)= 3ln(x)
f(x)= ln(x - 3)
f(x)= ln(x) + 3
A vertical shift upward is implemented by adding a constant to the function. Thus, f(x)= ln(x) + 3 shifts the graph upward by 3 units without altering its shape.
Which transformation of f(x)= x^2 results in a y-intercept of 7?
f(x)= x^2 - 7
f(x)= 7x^2
f(x)= (x+7)^2
f(x)= x^2 + 7
Adding 7 to f(x)= x^2 results in the function f(x)= x^2 + 7, which shifts the graph upward so that the y-intercept is 7. The other options modify the graph in different ways.
Identify the graph of the piecewise function f(x)= { x+2 for x < 0, x^2 for x ≥ 0 }.
A single smooth quadratic graph
A graph with a line for x < 0 and a parabola that seamlessly connect at (0,2)
A continuous graph where the line and parabola meet at (0,2)
A graph with a line for x < 0 ending in an open circle at (0,2), and a parabola for x ≥ 0 starting at (0,0)
The piecewise function has two distinct parts: a line (x+2) for x < 0 and a parabola (x^2) for x ≥ 0. Since these parts do not meet at the same point at x = 0, there is a jump discontinuity, correctly described in option A.
Determine the function that represents a vertical compression of f(x)= sin(x) by a factor of 1/2 combined with a reflection over the x-axis.
f(x)= -1/2 sin(x)
f(x)= 1/2 sin(x)
f(x)= sin(x)/2
f(x)= -2 sin(x)
A vertical compression by 1/2 multiplies the output of the function by 1/2, while a reflection over the x-axis multiplies the output by -1. Combining these transformations gives f(x)= -1/2 sin(x).
Which function represents a horizontal compression of f(x)= cos(x) by a factor of 2?
f(x)= cos(x) - 2
f(x)= cos(2x)
f(x)= cos(x/2)
f(x)= 2cos(x)
A horizontal compression by a factor of 2 is achieved by multiplying the variable inside the cosine function by 2. Therefore, f(x)= cos(2x) compresses the graph horizontally.
Find the equation of a quadratic function whose graph has a vertex at (-1, 5) and passes through the point (1, 1).
f(x)= (x-1)^2 + 5
f(x)= - (x-1)^2 + 5
f(x)= - (x+1)^2 + 5
f(x)= (x+1)^2 + 5
Using the vertex form, f(x)= a(x - h)^2 + k, with vertex (-1, 5) gives f(x)= a(x+1)^2 + 5. Substituting the point (1, 1) yields a = -1, and thus the function is f(x)= - (x+1)^2 + 5.
A rational function f(x)= (x-2)/(x^2-4) is simplified further. What is its simplified form along with its domain restrictions?
f(x)= 1/(x+2) with x ≠2 and x ≠-2
f(x)= 1/(x+2) with x ≠-2
f(x)= 1/(x-2) with x ≠2
f(x)= (x-2)/(x+2)
The denominator factors as (x-2)(x+2), and canceling the (x-2) terms (while noting x ≠2) leads to f(x)= 1/(x+2). However, the original function is undefined for both x = 2 and x = -2.
Which of the following describes the effect on the graph of f(x)= log(x) when its argument is replaced by 3(x-1)?
A horizontal shift left by 1 unit and a horizontal stretch by a factor of 3
A vertical shift upward by 3 units
A horizontal shift right by 1 unit and a horizontal compression by a factor of 1/3
A horizontal shift right by 3 units with no compression
Replacing x with 3(x-1) in log(x) results in two transformations: a horizontal shift right by 1 unit (due to (x-1)) and a horizontal compression by a factor of 1/3 (because of the multiplier 3). The other options do not capture both changes correctly.
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Study Outcomes

  1. Analyze the relationship between function equations and their graphs.
  2. Identify key features such as intercepts, slopes, and curves on function graphs.
  3. Match functions with their corresponding graphical representations accurately.
  4. Interpret changes in function parameters by observing variations in graph behavior.
  5. Apply critical thinking skills to assess and verify graphical information.

Quiz: Which Is the Graph of Function (100) Cheat Sheet

  1. Master common function shapes - Get to know the look of linear (y = x), quadratic (y = x²), cubic (y = x³), square root (y = √x), cube root (y = ∛x) and reciprocal (y = 1/x) graphs like a pro. Spotting these shapes first speeds up problem solving and boosts your confidence. GreenEMath practice test
  2. Practice graph transformations - Learn how shifts, reflections, stretches and compressions change your graphs so you can tweak functions at will. For example, y = (x - 2)² shifts the parabola two units to the right, and y = -2x flips and stretches it. AnalyzeMath transformations
  3. Identify domain and range - Become fluent in finding all possible x‑values (domain) and y‑values (range) of a function. For instance, y = √x only exists when x ≥ 0, so both domain and range start at zero and go up. GreenEMath domain & range
  4. Use function notation - Treat f(x) like a machine where x goes in and a value pops out. If f(x) = 2x + 3, plugging in f(2) gives you 7, so you're speaking "function" fluently! EduBirdie notation guide
  5. Apply the vertical line test - Draw vertical lines through your graph to see if you ever hit it more than once. If you do, it's not a function - no double dipping allowed! Varsity Tutors test
  6. Tackle composite functions - Dive into f∘g by plugging one function into another: if f(x)=x² and g(x)=x+1, then (f∘g)(x)=(x+1)². This builds your skills for chaining functions in one slick move. Pearson composites
  7. Spot even vs. odd functions - Know that even functions (like y=x²) mirror across the y-axis and odd ones (like y=x³) spin around the origin. This symmetry hack helps you predict graph behavior. Varsity Tutors symmetry
  8. Match functions to graphs - Train with quizzes and drills to link equations and their pictures instantly. The more you practice, the more "graph-vision" you'll develop! ChiliMath quiz
  9. Identify key graph features - Learn to spot intercepts, asymptotes and where curves climb or fall. For example, y=1/x has vertical and horizontal asymptotes at x=0 and y=0, making it an x‑and‑y barrier champ. GreenEMath features
  10. Use interactive resources - Boost retention with online tools, practice tests and dynamic problems that keep you engaged. A little daily graph-play goes a long way toward exam success! Pearson interactive practice
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