For the data $(1, 2),\ (2, 5),\ (3, 10),\ (4, 17)$, the first differences are $3, 5, 7$. What are the second differences, and what function family does this suggest?

Second differences are $2$; Quadratic

Second differences are $2$; Linear

Second differences are $3$; Exponential

Second differences are $2$; Exponential

A dataset has first differences of $2, 4, 8, 16$. Which method should you apply next to correctly identify the function family?

Check if the second differences are constant

Check if the successive ratios are constant

Check if the first differences are constant

Comparing Linear, Exponential, and Quadratic Functions Practice — Grade 8 math

Lesson 6: Comparing Linear, Exponential, and Quadratic Functions — Practice Questions

1. A table of data has evenly spaced $x$-values. The first differences of the $y$-values are $5, 5, 5, 5$. Which function family best models this data?
- A. Linear
- B. Quadratic
- C. Exponential
- D. None of the above
2. Consider the data: $(0, 2),\ (1, 6),\ (2, 18),\ (3, 54)$. The successive ratios between consecutive $y$-values are all equal to ___.
3. For the data $(1, 2),\ (2, 5),\ (3, 10),\ (4, 17)$, the first differences are $3, 5, 7$. What are the second differences, and what function family does this suggest?
- A. Second differences are $2$; Quadratic
- B. Second differences are $2$; Linear
- C. Second differences are $3$; Exponential
- D. Second differences are $2$; Exponential
4. The data $(0, 5),\ (1, 8),\ (2, 11),\ (3, 14)$ has evenly spaced $x$-values. The constant first difference is ___.
5. A dataset has first differences of $2, 4, 8, 16$. Which method should you apply next to correctly identify the function family?
- A. Check if the second differences are constant
- B. Check if the successive ratios are constant
- C. Check if the first differences are constant
- D. No further analysis is needed
6. What is the average rate of change of the function $f(x) = 4x - 1$ over the interval from $x=2$ to $x=5$? \nAnswer: ___
7. Calculate the average rate of change for the function $g(x) = x^2 + 1$ on the interval from $x=1$ to $x=4$. \nAnswer: ___
8. For a linear function like $f(x) = -3x + 8$, what is its average rate of change over any interval?
- A. -3
- B. 8
- C. 5
- D. It depends on the interval
9. What is the average rate of change of the exponential function $h(x) = 2^x$ from $x=2$ to $x=4$? \nAnswer: ___
10. Which of the following functions has the greatest average rate of change over the interval from $x=3$ to $x=5$?
- A. $f(x) = 5x$
- B. $g(x) = x^2$
- C. $h(x) = 2^x$
- D. The rates are all equal