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Grade 9 Quiz: Functions & Graphs — Easy Version 2
Grade 9 · MathSheets Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Function Notation with Graphs & Tables: The graph shows y = f(x). Find x when f(x) = -1.
Answer: -1
✓ Correct!
Not quite. The answer is
💡 How to solve: Function Evaluation
Replace every x in the rule with the given number, using parentheses around negative numbers. Then simplify using order of operations: exponents first, then multiplication, then addition and subtraction.
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If f(x) = 3x + 10, find f(-4).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Exponential Functions: Growth & Decay
An exponential function has the form y = a(b)x: a is the starting value and b is the number you multiply by each step. If b > 1 it is growth; if 0 < b < 1 it is decay. A growth rate r gives b = 1 + r, and a decay rate r gives b = 1 - r (write r as a decimal).
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f(x) = 3x. Find f(2).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Arithmetic Sequences
In an arithmetic sequence you add the same number d (the common difference) each time. The nth term is a_n = a_1 + (n - 1)d. Simplify it to get a rule like a_n = 3n + 2.
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Find the common difference of the sequence 4, 8, 12, 16, ...
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Direct & Inverse Variation
For direct variation, y = kx: find k = y ÷ x from the given pair, then multiply k by the new x. For inverse variation, y = k ÷ x: find k = x × y, then divide k by the new x.
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If y varies directly with x, and y = 4 when x = 1, find y when x = 4.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Standard Form & Intercepts
To find the x-intercept, set y = 0 and solve for x; to find the y-intercept, set x = 0 and solve for y. To change Ax + By = C to slope-intercept form, solve for y. To change y = mx + b to standard form, move the x-term to the left and clear any fractions.
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Find the x-intercept of -x - 3y = -3.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Function Notation with Graphs & Tables
f(3) means "the output of f when the input x is 3". On a graph, go to x = 3 on the x-axis and read the y-value of the graph there. To solve f(x) = 4, find where the graph (or table) has output 4 and read the x-value.
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The graph shows y = f(x). Find f(2).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Slope & Graphing Linear Equations
To find the slope through two points, use m = (y₂ - y₁) ÷ (x₂ - x₁). To find the y-intercept from a slope and a point, substitute into y = mx + b and solve: b = y - mx.
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Find the slope of the line through A(-6, -10) and B(-4, -2).
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✓ Correct!
Not quite. The answer is
💡 How to solve: Writing Equations of Lines (Point-Slope Form)
Point-slope form is y - y1 = m(x - x1), using the slope m and a point (x1, y1) on the line. To get slope-intercept form y = mx + b, distribute m and add y1 to both sides. With two points, first find the slope m = y2 - y1x2 - x1.
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Write an equation in slope-intercept form of the line with slope 1 that passes through (3, 1).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Graphing Quadratic Functions (Vertex & Axis of Symmetry)
For y = ax2 + bx + c, the axis of symmetry is x = -b2a. Substitute that x-value into the equation to get the y-coordinate of the vertex. If a > 0 the parabola opens up and the vertex is a minimum; if a < 0 it opens down and the vertex is a maximum.
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What is the vertex of the parabola?
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✓ Correct!
Not quite. The answer is
💡 How to solve: Graphing Absolute Value Functions
The graph of y = a|x - h| + k is a V with its vertex at (h, k). Watch the sign inside the bars: |x + 3| means h = -3. If a is positive the V opens up and k is the minimum value; if a is negative it opens down and k is the maximum. The axis of symmetry is x = h. The right-hand branch has slope a and the left-hand branch has slope -a. For the y-intercept substitute x = 0; for the x-intercepts set y = 0 and solve.
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What is the vertex of the absolute value graph?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Grade 9 Quiz: Functions & Graphs — Easy Version 2
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.