Graphs of functions

1. For y = 2x - 3, what is y when x = 4?

1. 5
2. 8
3. 11
4. -5

2. A table is being constructed for y = x^2 - x - 2. Which y-value belongs to x = -2?

1. -8
2. 4
3. 0
4. 8

3. A straight line passes through (-1, -5) and (3, 7). What is its gradient?

1. 1/3
2. 2
3. 3
4. 4

4. What is the y-intercept of the line y = -2x + 6?

1. (-2, 0)
2. (0, -2)
3. (0, 3)
4. (0, 6)

5. The graph of y = x^2 - 5x + 6 crosses the x-axis at exactly (2, 0) and (3, 0). What are its roots?

1. x = 2 or 3
2. x = -3 or -2
3. x = 0 or 6
4. x = 5 or 6

6. For y = (x + 1)^2 - 4, which coordinate is the minimum turning point?

1. (1, -4)
2. (-1, -4)
3. (-1, 4)
4. (4, -1)

7. A quadratic has roots at x = 1 and x = 5. What is the equation of its vertical line of symmetry?

1. x = 2
2. x = 4
3. x = 3
4. y = 3

8. For y = x^3 - 4x, which list gives all x-axis intersection coordinates?

1. (-4, 0), (0, 0), (4, 0)
2. (-2, 0), (2, 0)
3. (0, -2), (0, 0), (0, 2)
4. (-2, 0), (0, 0), (2, 0)

9. For y = -2x^3, what happens to y as x becomes a large positive number?

1. y becomes a large negative number
2. y becomes a large positive number
3. y approaches 0 from above
4. y remains equal to -2

10. Which vertical asymptote belongs to y = 8/x?

1. x = -8
2. x = 0
3. y = 0
4. y = 8

11. Which coordinate lies on y = 8/x when x = -4?

1. (-4, 2)
2. (-2, -4)
3. (-4, -2)
4. (4, -2)

12. The points (-3, 1), (-1, 9), (1, 9) and (3, 1) lie on y = 9/x^2. Which symmetry do these coordinates show?

1. Symmetry about the x-axis
2. Symmetry about y = x
3. No symmetry
4. Symmetry about the y-axis

13. For y = 12/sqrt(x), what is y at x = 9?

1. 4
2. 4/3
3. 3
4. 6

14. What is the real-number domain of y = sqrt(x)?

1. x < 0
2. x >= 0
3. x <= 0
4. x > 0

15. For y = 3(2^x) + 1, what is y when x = 3?

1. 10
2. 16
3. 25
4. 24

16. For y = 7(3^x) + 5, which horizontal line is the graph's asymptote as x decreases without bound?

1. x = 0
2. y = 0
3. y = 7
4. y = 5

17. A quantity is modelled by Q = 160(2^(-t)), where t is measured in hours. What is Q at t = 3 hours?

1. 20
2. 10
3. 40
4. 80

18. An exponential graph contains the coordinates (0, 6), (1, 12) and (2, 24). By what factor does y change whenever x increases by 1?

1. It increases by 6
2. It doubles
3. It triples
4. It is squared

19. The curve y = x^2 - 1 and the line y = x + 1 intersect exactly at (-1, 0) and (2, 3). What are the graphical solutions of x^2 - 1 = x + 1?

1. x = 0 or x = 3
2. y = -1 or y = 2
3. x = -1 or x = 2
4. x = 1 or x = -2

20. All the x-axis intersections of a curve are exactly (-3, 0), (1, 0) and (4, 0). Which list gives all roots of the function?

1. -3, 0 and 4
2. 0, 1 and 4
3. 3, -1 and -4
4. -3, 1 and 4

21. A tangent to a curve passes through the explicit points (2, 1) and (6, 13). What is the tangent's gradient?

1. 3
2. 2
3. 4
4. 12

22. At a stated contact point, a curve has tangent y = -2x + 7. What is the curve's estimated gradient there?

1. -7
2. -2
3. 2
4. 7

23. A graph is described as one smooth curve with a single minimum turning point, symmetry about a vertical line and two arms that rise. Which family fits this description?

1. Linear
2. Reciprocal
3. Quadratic
4. Exponential

24. A table is constructed for y = 2x^3 - x. Which coordinate belongs to x = -2?

1. (-2, -18)
2. (-2, 14)
3. (2, -14)
4. (-2, -14)