Testinar Grade 8 math

What Is a Function?

Learn to reason about and solve Grade 8 problems involving What Is a Function?.

CH04-01 Functions and Linear Relationships

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Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

The table below shows a relation. Is it a function?
1. No, because the outputs are larger than inputs.
2. Yes, each input has exactly one output.
3. No, because \(y\) values increase by 3.
4. Yes, because all values are positive.
Which table represents a function?
1. Table A, because it has more inputs.
2. Table B, because each input has exactly one output.
3. Both tables are functions.
4. Neither table is a function.
Which graph does NOT represent a function?
1. A line passing through \((0,2)\) and \((2,6)\).
2. A horizontal line at \(y = 5\).
3. A curve shaped like a sideways parabola opening right.
4. A diagonal line with negative slope.
What is the domain of the graphed function?
1. \(\{0, 1, 2, 3, 4\}\)
2. \([0, 4]\)
3. \(\{1, 3\}\)
4. All real numbers
A vertical line test is performed on the graph below. How many times does a vertical line intersect the curve?
1. Zero times (the line misses the curve).
2. Once (the line intersects at one point).
3. Twice (the line intersects at two points).
4. More than twice.
A function machine multiplies the input by 2 and adds 3. If the input is \(x\), what is the output?
1. \(2x + 3\)
2. \(2(x + 3)\)
3. \(3x + 2\)
4. \(x + 5\)
Which table represents a function where the output is always greater than the input?
1. Neither table.
2. Table A only.
3. Table B only.
4. Both tables.
Is the graph of a straight line passing through \((1,2)\) and \((3,6)\) a function?
1. No, it is not steep enough.
2. Yes, because it is a straight line.
3. Yes, it passes the vertical line test.
4. No, because the slope is positive.

Teacher and parent reference

Answer key and explanations

B. Yes, each input has exactly one output.
Each input value (\(1, 2, 3, 4\)) corresponds to exactly one output value (\(3, 6, 9, 12\)). The relationship is \(y = 3x\), making it a function.
B. Table B, because each input has exactly one output.
Table A has input 2 appearing twice with different outputs (5 and 6), so it is not a function. Table B has each unique input paired with exactly one output.
C. A curve shaped like a sideways parabola opening right.
A sideways parabola (opening right or left) fails the vertical line test because some vertical lines intersect it twice. The other options all pass the vertical line test.
B. \([0, 4]\)
The segment starts at \(x=0\) and ends at \(x=4\). The domain includes all \(x\)-values in this range: \([0, 4]\).
B. Once (the line intersects at one point).
The parabola opens upward and any vertical line intersects it at most once (or once in the visible region shown). This confirms it is a function.
A. \(2x + 3\)
Multiply by 2 first: \(2x\). Then add 3: \(2x + 3\).
B. Table A only.
Table A: outputs are \(3, 5, 7, 9\) and inputs are \(1, 2, 3, 4\) — all outputs are greater. Table B: when \(x=0\), \(y=0\) (equal, not greater).
C. Yes, it passes the vertical line test.
Non-vertical straight lines pass the vertical line test and are functions. Every vertical line intersects the graph at most once.