Question

Plot the data for the functions ƒ(x) and g(x) on a grid. x -2 -1 0 1 2 ƒ(x) 1 4 16 x -1 0 1 2 3 g(x) 3 4 5 6 7 b. Identify each function as linear, quadratic, or exponential, and use complete sentences to explain your choices. c. Describe what happens to the function values in each function as x increases from left to right. d. At what value(s) of x are the function values equal? If you cannot give exact values for x, give estimates.

Answer 1

1. exponential,The function ƒ(x) is exponential because its graph approaches but does not cross the negative x axis; ƒ(x) > 0 for all values of x. The function g(x) is linear since g(x) increases by the same amount as x increases in steps of one unit.

2. As x gets more negative, ƒ(x) gets smaller and approaches zero. At x = 0, ƒ(x) = 1. As x gets more positive, ƒ(x) gets larger. At x = -4, g(x) = 0. For values of x > -4,g(x) increases by one as the values of x increase by one.

3. The function values appear to be equal at about x = -4 and at about x = 1.2., The linear and exponential functions intersect, or have the same value of y, at approximately x = 1.8 and x = -2.8.

Explanation:

Answer 2

Part A:

The plot for the function f(x) and g(x) is attached. The purple curve represents f(x) and the black line represents g(x).



Part B:

The graph of f(x) shows that f(x) is an exponential function.
The graph of g(x) shows that g(x) is a linear function.



Part C:

As x increases from left to right, the function f(x) increases very rapidly.
As x increases from left to right, the function f(x) increases at a constant rate.



Part D:

From the graph it can be seen than the valus of x for which the values of the function are equal are: x = -4 and x = 1.19.