a. Plot the data for the functions ƒ(x) and g(x) on a grid.

Question

a. 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

A. plot the respective points on a graph first using x to determine left to right location and y to determine the up to down locations.

B. The f(x) function is exponential and most likely the function 4^x power. To figure this out mathematically, we can check how much Y is increasing by how much X is increasing, and in this case, X is increasing dramatically. We can rule out quadratic since I am assuming at 0, the answer is 1, which 4^0 power is 1.

for g(x), its a linear function, since the amount y changes is constant in respect to how much x changes, so if x increases from -2 to 2, y changes from 3 to 7, which means g(x) increases by 1. We can take another 2 points and compare the slope or change and see this is still true.

C. For f(x) since its exponential, it'll increase to infinity and change much more rapidly. Similar to a car which is accelerating. For g(x) its increasing constantly to infinity, but at a standard rate so with the same car analogy, its increasing its distance, but staying at the same speed.

D. to figure out when these graphs intersect or have the same values at certain X, we can look at the plotted graph to see where they intersect. You can also plug them equal to each other and see at which values they might equal each other. For example 4^x = x+4, at x=1, f(x) is 4 while g(x) is 5, but at x=2, f(x) is 16, while g(x) is 6, so they must intersect in between at 1<x<2.