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Math 10C

Math 10C · Worksheets

Mixed review · Relations and linear functions

Ten questions of mixed difficulty, covering Linear functions, Relations and functions. Print it, or work through it on screen — the answer key starts on its own page.

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Mixed review · Relations and linear functions

Math 10C · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A line through (1, 2) and (3, 8) has slope

    1. a) 1/3
    2. b) 3
    3. c) 6
    4. d) 2

  2. If f(x) = x² + 1 and f(a) = 10, then a could be

    1. a) 10
    2. b) 9
    3. c) 3 or −3
    4. d) ±√10

  3. A relation is a function when

    1. a) the graph is a straight line
    2. b) each input has exactly one output
    3. c) each output has exactly one input
    4. d) the graph passes through the origin

  4. The equation of a line with slope −2 through (0, 5) is

    1. a) y = −2x − 5
    2. b) y = 5x − 2
    3. c) y = 2x + 5
    4. d) y = −2x + 5

  5. The range of the relation graphed as a parabola with vertex (2, −3) opening upward is

    1. a) y ≥ −3
    2. b) x ≥ 2
    3. c) all real numbers
    4. d) y ≤ −3

  6. A horizontal line has slope

    1. a) 0
    2. b) undefined
    3. c) 1
    4. d) −1

  7. For the graph of a line with no restrictions, the domain is

    1. a) the y-intercept
    2. b) x ≥ 0
    3. c) only whole numbers
    4. d) all real numbers

  8. The solution to a system of two linear equations is

    1. a) the point where the lines intersect
    2. b) always the origin
    3. c) the y-intercepts added together
    4. d) the slope of both lines

  9. A relation shows the cost of buying n tickets at $12 each. A sensible domain is

    1. a) all real numbers
    2. b) negative numbers only
    3. c) whole numbers from 0 upward
    4. d) numbers between 0 and 1

  10. If f(x) = x² − 2x, then f(−3) is

    1. a) 15
    2. b) 3
    3. c) −15
    4. d) −3

Answer key · Mixed review · Relations and linear functions

Math 10C · maddyhelps.com

  1. b) 3 — Slope = (8 − 2)/(3 − 1) = 6/2 = 3. Subtract the coordinates in the same order top and bottom; swapping one of them flips the sign.
  2. c) 3 or −3 — Set x² + 1 = 10, so x² = 9 and x = ±3. Both work, because squaring removes the sign — giving only 3 loses half the answer.
  3. b) each input has exactly one output — Inputs may not be shared out; outputs may. Two different x-values can give the same y and it is still a function — the rule is about x, not y.
  4. d) y = −2x + 5 — The point is on the y-axis, so it is the intercept and slope-intercept form can be written straight down. A negative slope means the line falls from left to right, which matches.
  5. a) y ≥ −3 — The vertex is the lowest point, so no y-value below −3 is reached, and every value above it is. Range describes y; the x ≥ 2 answer is describing the wrong axis.
  6. a) 0 — There is no rise, so the slope is 0 ÷ run = 0. A <i>vertical</i> line is the other case: the run is zero, and dividing by zero makes its slope undefined rather than zero.
  7. d) all real numbers — A line continues forever in both directions, so every x-value works. The exception is a horizontal line, which is still all real numbers for domain but has a single value for range.
  8. a) the point where the lines intersect — A solution must satisfy both equations at once, which graphically means lying on both lines. So the answer is a point, with two coordinates.
  9. c) whole numbers from 0 upward — You cannot buy half a ticket or a negative number of them. Domain in a word problem is set by the situation, not by the algebra, and saying so is usually worth a mark.
  10. a) 15 — Substitute carefully with brackets: (−3)² − 2(−3) = 9 + 6 = 15. Both minus signs are easy to lose — (−3)² is positive 9, and subtracting a negative adds.