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Quizzes > High School Quizzes > Mathematics

Master Graphing Functions Practice Quiz

Sharpen skills with interactive practice questions

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art depicting trivia quiz on graphing functions for high school math students.

What does the y-intercept of a function's graph represent?
The value of y when x = 0.
The value of x when y = 0.
The slope of the line.
The maximum value of the function.
The y-intercept is the point where the graph crosses the y-axis, which occurs when x is 0. Option a is correct because it accurately defines this intercept.
Which graph represents a linear function?
A graph containing a straight line.
A graph containing a smooth curve that opens upward.
A graph with two separate lines.
A graph forming a circle.
A linear function is characterized by a straight line when graphed. Option a is correct because it reflects the direct relationship between x and y with constant rate of change.
For the line with equation y = 3x + 2, what is the slope?
3
2
1/3
-3
In the slope-intercept form of a linear equation, y = mx + b, the coefficient m represents the slope. Option a is correct because the slope is clearly identified as 3.
What is the effect on a graph when the constant term b in y = mx + b is increased?
The graph shifts upward.
The graph shifts downward.
The graph rotates.
The graph becomes steeper.
Increasing the constant term b in the equation results in a vertical translation of the graph. Option a is correct because it indicates that the entire graph moves upward.
Which of these is the graph of a function?
A curve that passes the vertical line test.
A circle.
A sideways parabola.
A set of discrete, unconnected points.
For a graph to represent a function, every vertical line drawn through the graph must intersect it at most once. Option a is correct because it meets the vertical line test requirement.
How do you determine if a graph represents a function?
By using the vertical line test.
By checking if every x value has more than one y value.
By verifying if the graph is symmetric about the y-axis.
By determining if the graph is a straight line.
The vertical line test is a standard method to determine if a graph represents a function. Option a is correct because it ensures that each x-value corresponds to only one y-value.
Given the function f(x) = (x - 1)^2, what is the vertex of its graph?
(1, 0)
(0, -1)
(-1, 0)
(0, 1)
The function is in vertex form, where the vertex (h, k) is directly read from the expression (x - 1)^2. Option a is correct because it identifies (1, 0) as the vertex.
What transformation occurs when the function f(x) is replaced by f(x) + 4?
Vertical shift upward by 4 units.
Horizontal shift to the right by 4 units.
Vertical stretch by a factor of 4.
Reflection across the x-axis.
Adding a constant to the function f(x) results in shifting the graph vertically. Option a is correct because it correctly describes a shift upward by 4 units.
In the function y = -2x + 6, what does the -2 represent?
The slope, indicating a decrease as x increases.
The y-intercept.
A vertical stretch factor.
The x-intercept.
In the linear equation y = mx + b, the coefficient m represents the slope. Option a is correct because -2 shows a negative slope, meaning the function decreases as x increases.
If a function is defined by f(x) = 1/(x-3), what is a vertical asymptote of its graph?
x = 3
y = 3
x = -3
y = -3
Vertical asymptotes occur where the denominator of a rational function is zero. Option a is correct because setting x - 3 equal to zero gives x = 3.
Which of the following equations represents a parabola?
y = x^2 + 2x + 1
y = 2x + 3
y = 1/x
y = |x|
A quadratic equation of the form y = ax^2 + bx + c represents a parabola. Option a is correct because it clearly fits the quadratic form.
How does the graph of y = √x differ from the graph of y = x^2?
y = √x is the inverse of y = x^2 for x ≥ 0.
y = √x is a parabola opening upward.
y = √x has a vertex at (0,0) while y = x^2 does not.
y = √x is symmetric about the y-axis while y = x^2 is not.
The graph of y = √x is the inverse of y = x^2 when considering non-negative x values. Option a is correct because it captures the inverse relationship between the two functions.
Which of these graphs passes the vertical line test?
A graph where every vertical line intersects the graph at most once.
A circle.
The graph of x = y^2.
A graph with a sideways parabola.
The vertical line test ensures that each x-value maps to only one y-value. Option a is correct because it describes the necessary condition for a graph to be a function.
What does the horizontal shift in the function f(x - 3) indicate?
The graph is shifted to the right by 3 units.
The graph is shifted to the left by 3 units.
The graph is shifted upward by 3 units.
The graph is reflected, not shifted.
Replacing x with (x - 3) in the function results in a horizontal translation. Option a is correct because it properly indicates a shift to the right by 3 units.
Which function transformation represents a reflection over the x-axis?
Multiplying the function by -1, i.e., -f(x).
Replacing x with -x, i.e., f(-x).
Adding a negative constant, i.e., f(x) - c.
Taking the reciprocal of the function, i.e., 1/f(x).
A reflection over the x-axis is achieved by multiplying the entire function by -1. Option a is correct because it directly reflects every output value, turning positive values negative and vice versa.
Consider the function f(x) = 2(x - 1)^2 - 5. What is the vertex of this parabola and its axis of symmetry?
Vertex is (1, -5) with axis x = 1.
Vertex is (-1, -5) with axis x = -1.
Vertex is (1, 5) with axis x = 1.
Vertex is (5, 1) with axis x = 5.
This function is written in vertex form, f(x) = a(x - h)^2 + k, where (h, k) is the vertex. Option a is correct because it identifies the vertex (1, -5) and the axis of symmetry as the line x = 1.
The function g(x) = |x - 4| + 2 is graphed on the coordinate plane. Which statement is true regarding its graph?
It has a vertex at (4, 2) and opens upward.
It has a vertex at (-4, 2) and opens downward.
It has a vertex at (4, -2) and opens upward.
It has a vertex at (2, 4) and opens to the right.
The absolute value function |x - 4| is minimized when x = 4, making (4, 0) the basic vertex before translation. Adding 2 shifts the graph upward, resulting in a vertex at (4, 2); therefore, option a is correct.
Given a function f(x) that is known to be even, which of the following must be true about its graph?
It is symmetric about the y-axis.
It is symmetric about the x-axis.
It has its vertex at the origin.
It passes the vertical line test twice.
An even function satisfies the condition f(x) = f(-x), which means its graph is symmetric about the y-axis. Option a is correct because this symmetry is the defining property of even functions.
For the rational function h(x) = (2x + 3)/(x - 1), what are its vertical and horizontal asymptotes?
Vertical: x = 1, Horizontal: y = 2.
Vertical: x = 2, Horizontal: y = 1.
Vertical: y = 1, Horizontal: x = 2.
Vertical: x = -3, Horizontal: y = 2.
The vertical asymptote is determined by setting the denominator equal to zero, which yields x = 1. The horizontal asymptote is given by the ratio of the leading coefficients (2/1 = 2), so option a is correct.
Consider the composite function (f ∘ g)(x) = f(g(x)) where f(x) = x^2 and g(x) = 3x - 1. What is the simplified form of (f ∘ g)(x)?
9x^2 - 6x + 1
3x - 1
x^2 + 3x - 1
9x^2 + 1
To compute the composite function, substitute g(x) into f(x): f(g(x)) = (3x - 1)^2. Expanding this expression yields 9x^2 - 6x + 1, so option a is correct.
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Study Outcomes

  1. Graph functions accurately using interactive tools.
  2. Identify key features of different function types.
  3. Interpret graph behavior to assess function properties.
  4. Apply transformations to modify function graphs.
  5. Analyze graph information to solve function-related problems.

Graphing Functions Cheat Sheet

  1. Understanding Functions - A function pairs each input with exactly one output, forming the backbone of graphing and analysis. Mastering this ensures you can accurately predict how changes in x affect y. Common Core Mapping for Functions
  2. Function Notation - Notation like f(x) streamlines how we define and work with functions, making evaluations and transformations cleaner. Grasp these conventions to boost your problem-solving speed. Explore Function Notation
  3. Key Graph Features - Identifying intercepts, intervals of increase or decrease, and relative extrema reveals a function's behavior at a glance. Being able to read these features lets you interpret real‑world data effectively. Interpreting Graph Features
  4. Graphing Practice - Drawing linear, quadratic, and exponential curves helps you recognize patterns and anticipate shapes. Regular drills turn confusion into confidence on every axis. Practice Problems on Graphing
  5. Function Transformations - Shifts, reflections, stretches, and compressions change a graph's look while keeping its core intact. Learning these moves is like mastering dance steps for your graphs. Review Transformations
  6. Domain and Range - Defining allowable inputs (domain) and possible outputs (range) keeps your graphs realistic and accurate. This knowledge is crucial when modeling anything from budgets to physics. Domain & Range Guide
  7. Average Rate of Change - This measurement shows how fast a function's value shifts over an interval, setting the stage for calculus concepts. It's like calculating your car's average speed on a road trip. Rate of Change Lessons
  8. Piecewise Functions - Different rules apply to different parts of the domain, making these functions perfect for modeling real-life scenarios with changing conditions. Practice plotting each segment for clarity. Graph Piecewise Functions
  9. Absolute Value Graphs - Characterized by a V‑shape, these graphs flip and shift with transformations, offering insight into distance‑based relationships. Understanding them helps with error analysis and optimization. Absolute Value Lessons
  10. Exponents & Logarithms - Recognizing these inverse operations unlocks a world of exponential growth and decay problems, from population models to finance. Solidify this duo to conquer advanced math challenges. Exponents & Logs Guide
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