Question

The following is a graph of the function f(x) = 2^x. The graph was transformation to h(x) = 1/7×2^x. How does this change the graph?​

Answer 1

The graph of h(x) = 1/7×2^x would be the same as the graph of f(x) = 2^x, but it would be vertically scaled down by a factor of 1/7. This means that all the points on the graph of h(x) would have the same x-coordinates as the corresponding points on the graph of f(x), but their y-coordinates would be 1/7 times smaller. For example, the point (1,2) on the graph of f(x) would be located at (1,1/7) on the graph of h(x).

Answer 2

The graph of h(x) = 1/7×2^x will be shifted to the left and compressed compared to the graph of f(x). The y-intercept of h(x) will be 1/7, whereas the y-intercept of f(x) is 1. The graph of h(x) will also have a much smaller range than the graph of f(x).

Explanation:

The equation of a graph is given by y=f(x). After transformation, the equation changes to y=h(x).

h(x) = 1/7×2^x

h(x) = 1/7 × (2^x)

h(x) = 1/7 * 2^x

h(x) = (1/7)2^x

=> y = (1/7)2^x

=> y = 1/7 (2^x)

Therefore, the graph of h(x) = 1/7×2^x will be shifted to the left and compressed compared to the graph of f(x). The y-intercept of h(x) will be 1/7, whereas the y-intercept of f(x) is 1. The graph of h(x) will also have a much smaller range than the graph of f(x).