Linear vs. exponential functions & intersections of graphs

1. Linear vs. exponential functions&intersections of graphs

6. The table and the graph show an insect population that increases over time.

7. A function rule that describes the pattern above is f(x) = 2(3)x. This type of function, in which the independent variable appears in an exponent, is an exponential function. Notice that 2 is the starting population and 3 is the amount by which the population is multiplied each day.

8. Remember that linear functions have constant first differences. Exponential functions do not have constant differences, but they do have constant ratios. As the x-values increase by a constant amount, the y-values are multiplied by a constant amount. This amount is the constant ratio and is the value of b in f(x) = abx.

9. Linear, Exponential, or Neither

10. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.#1. Linear

11. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.#2. Exponential

12. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.#3. This function is decreasing at a constant rate. Linear

13. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.#4. A person’s height as a function of a person’s age (from age 0 to100). Neither

14. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.#5. Linear

15. For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer.#6. Each term in a sequence is exactly 1/3 of the previous term. Exponential

16. Intersections of graphs

17. Points of Intersection