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Quizzes > Quizzes for Business > Education

Take the 8th Grade Functions and Graphing Quiz

Boost Your Understanding of Functions and Graphs

Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art illustrating 8th grade functions and graphing quiz theme

Are you ready to test your graphing skills and function fluency with this lively 8th grade functions quiz? Crafted for curious learners and classrooms alike, this practice makes mastering slopes, intercepts, and function types engaging. Students will gain confidence in plotting equations and interpreting graphs. Plus, every question can be freely customised in our editor to suit individual learning goals. For extra review, explore the 7th Grade Math Assessment Quiz or the 5th Grade General Knowledge Quiz , and browse all our quizzes.

Which of the following equations represents a nonlinear function?
y = 2x + 3
y = x^2 - 1
y = -5x + 4
y = \frac{1}{2}x - 7
A nonlinear function includes variables raised to a power other than 1. The term x^2 in y = x^2 - 1 makes it nonlinear. The other equations are linear because they have the form y = mx + b.
What is the slope of the line represented by y = 4x - 2?
4
-2
2
-4
In the slope-intercept form y = mx + b, m is the slope. Here m = 4, so the slope is 4. The constant -2 is the y-intercept, not the slope.
What is the y-intercept of the line y = -3x + 5?
5
-3
-5
3
In y = mx + b, b is the y-intercept. Here b = 5, so the line crosses the y-axis at (0, 5). The other numbers refer to slope or are incorrect.
For the function f(x) = 2x + 1, what is f(3)?
7
5
6
9
Substitute x = 3 into f(x): f(3) = 2(3) + 1 = 6 + 1 = 7. This direct substitution gives the correct output.
Which of the following functions has a constant rate of change?
y = 2x + 1
y = x^3
y = x^2 + 2
y = 4/x
A constant rate of change indicates a linear function of the form y = mx + b. The function y = 2x + 1 has a constant slope of 2. The other functions have varying rates of change.
A line passes through (0, -2) and (3, 4). What is its slope?
2
3
6/3
-2
Slope = (y2 - y1)/(x2 - x1) = (4 - (-2))/(3 - 0) = 6/3 = 2. Writing it as 6/3 emphasizes the calculation. All forms are equivalent, but 6/3 shows the work.
The line y = -x + 3 is shifted up by 2 units. What is the new equation?
y = -x + 5
y = -x + 1
y = -x - 5
y = x + 5
Shifting a graph up by 2 adds 2 to the y-value, so you add 2 to the constant term. -x + 3 becomes -x + 5. The slope remains unchanged.
Which equation represents a horizontal line?
y = 6
x = 6
y = 2x + 3
x + y = 1
A horizontal line has the form y = constant. The equation y = 6 is horizontal. The others describe vertical or slanted lines.
For f(x) = -2x + 4, what is f(-1)?
6
-6
2
-2
Substitute x = -1: f(-1) = -2(-1) + 4 = 2 + 4 = 6. This uses direct evaluation of the linear expression.
If the slope of a line increases, which of the following describes the new graph?
The line becomes steeper upward.
The line becomes shallower.
The y-intercept changes.
The line reflects across the y-axis.
A larger positive slope makes the line rise more sharply, so it appears steeper. The y-intercept stays the same unless explicitly changed.
Which function represents a direct proportional relationship?
y = 5x
y = 5x + 2
y = 2^x
y = x^2
A direct proportional relationship has no constant term, so y = kx. The function y = 5x fits that form. The other options have extra terms or different growth patterns.
A taxi charges a $3 base fee plus $2 per mile. Which equation models the cost C for m miles?
C(m) = 2m + 3
C(m) = 3m + 2
C(m) = 2m - 3
C(m) = 3m - 2
The cost increases by $2 for each mile, so the slope is 2. The base fee of $3 is the intercept, so C(m) = 2m + 3.
Which point lies on the graph of y = \tfrac{1}{2}x - 3?
(4, -1)
(2, 1)
(-2, -4)
(3, -1)
Substitute x = 4: y = 1/2·4 - 3 = 2 - 3 = -1. So (4, -1) is on the line. The other points do not satisfy the equation.
What is the y-intercept of f(x) = 3(x - 2) + 1?
-5
3
-6
1
Expand f(x) to 3x - 6 + 1 = 3x - 5, so the y-intercept is -5. The constant term after expansion is the intercept.
A line passes through A(1, 2) and B(4, k). If its slope is 3, what is k?
11
9
5
8
Slope = (k - 2)/(4 - 1) = 3, so k - 2 = 9 and k = 11. This ensures the rise over run equals 3.
Which value of m makes the line y = mx + 2 perpendicular to y = \tfrac{1}{2}x - 3?
-2
2
\tfrac{1}{2}
-\tfrac{1}{2}
Perpendicular slopes are negative reciprocals. The negative reciprocal of 1/2 is -2, so m = -2.
Original line: y = 2x - 1. It is shifted right by 3 units and up by 4 units. What is the new equation?
y = 2x - 3
y = 2x + 3
y = 2x + 5
y = 2x - 5
A right shift replaces x with (x - 3): y = 2(x - 3) - 1 = 2x - 6 - 1 = 2x - 7, then up 4 adds 4: 2x - 7 + 4 = 2x - 3.
If f(x) = ax + b, f(2) = 8 and f(-1) = 1, what are a and b?
a = 7/3, b = 10/3
a = 3, b = 2
a = 2, b = 4
a = 1/2, b = 7
Solve 2a + b = 8 and -a + b = 1. Subtracting gives 3a = 7, a = 7/3. Then b = 8 - 14/3 = 10/3.
A water tank drains at the rate V(t) = -5t + 100 liters. How much water remains after 12 minutes?
40 liters
-40 liters
160 liters
100 liters
Evaluate V(12): -5(12) + 100 = -60 + 100 = 40 liters remain. The negative coefficient indicates a drain over time.
0
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Learning Outcomes

  1. Identify linear and nonlinear functions from their graphs.
  2. Interpret slope and intercept values in various functions.
  3. Graph linear equations accurately on the coordinate plane.
  4. Analyze how changes in parameters affect graph shapes.
  5. Evaluate function outputs for given inputs with confidence.
  6. Apply function concepts to solve real-world problems.

Cheat Sheet

  1. Understand the difference between linear and nonlinear functions - Think of a straight road versus a winding mountain path: linear functions plot as straight lines with a constant rate of change, while nonlinear functions curve and change pace at every turn. Mastering this distinction sets you up to tackle any graph with confidence! onlinemathlearning.com
  2. Master the slope - intercept form of a linear equation: y = mx + b - Here's your secret weapon: 'm' tells you how steep the climb is, and 'b' shows where the line touches the y-axis. Once you see how these two pieces work together, creating and tweaking lines feels like a breeze! OpenStax Precalculus
  3. Learn to calculate the slope between two points - Grab any two spots on your line and plug them into (y₂ - y₝)/(x₂ - x₝) to find the slope. This simple formula tells you the line's tilt - positive for uphill, negative for downhill, and zero for flat! OpenStax Precalculus
  4. Practice graphing linear equations using the slope and y-intercept - Start at the y-intercept point, then "rise over run" using the slope to plot your next spots. Before you know it, you'll be sketching perfect lines faster than you can say "graphing"! OpenStax Precalculus
  5. Recognize how changes in "m" and "b" affect the graph - Crank up 'm' and your line gets steeper; tweak 'b' and it shifts up or down like a hot air balloon. Playing with these parameters is like having your own line lab - experiment away! OpenStax Precalculus
  6. Identify parallel and perpendicular lines by their slopes - Parallel lines are slope twins - they never meet. Perpendicular lines are the ultimate opposites, with slopes that multiply to - 1, making a perfect right angle! OpenStax Precalculus
  7. Understand the concept of a function and its notation - A function is like a magical machine: you drop in an input, and it spits out exactly one output every time. We usually call it f(x), where 'x' is your entry ticket to the show! Wikipedia
  8. Evaluate function outputs for given inputs confidently - Got a function rule? Just substitute your chosen x-value, do a bit of arithmetic, and - voilà - you've got the corresponding y. It's like solving a mini puzzle in one smooth step. Wikipedia
  9. Apply function concepts to solve real-world problems - From calculating how far you'll travel on a bike to predicting savings growth in your piggy bank, functions turn real scenarios into neat equations. Practice modeling a situation, and watch the math bring it to life! OpenStax Precalculus
  10. Practice interpreting and sketching graphs from verbal descriptions - Turn story problems into visual graphs by pinpointing your variables and their relationships. With each new scenario, you'll flex your graph-reading muscles and level up your math storytelling! Turito
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