Question

How does the graph of g(x) = 4ˣ + 5 compare to the function represented by the table below?

x: -2, -1, 0, 1, 2
h(x): 17, 16, 5, 4, 2, 5

A. The graph of g is a translation 16 units up from the graph of h.
B. The graph of g is a translation 49 units up from the graph of h.
C. The graph of g is a translation 4 units up from the graph of h.
D. The graph of g is a translation 4 units down from the graph of h.

Answer 1

The graph of g(x) = 4ˣ + 5 is a translation 4 units up from the function represented by the table.

Therefore, the correct answer is C.

Step-by-step explanation:

The graph of the function g(x) = 4ˣ + 5 would be a translation 4 units up from the function represented by the table.

To compare the two, we can look at the y-values for each x-value in the table. The table shows y-values of 17, 16, 5, 4, and 2 for x-values of -2, -1, 0, 1, and 2 respectively. If we substitute these x-values into g(x) = 4ˣ + 5, we get y-values of 17, 20, 9, 9, and 21. So, the y-values are 4 units higher for each x-value.

Therefore, the correct answer is C. The graph of g is a translation 4 units up from the graph of h.