Question

The table below represents a function. x 1 2 3 4 5 y 1 16 64 256 1,024 Which statement would best describe the graph of the function? The graph is a straight line that has a slope of 8. The graph is a horizontal line at y = 16. The graph starts flat but curves steeply upward. The graph is a parabola that opens upward.

Answer 1

Create a table with 3 columns as follows:

    x            y           f(x)
------  ---------  -------------
    1           1            ?
    2        16           4^2
    3        64          4^3
    4       256         4^4
    5      1024        4^5

Notice that when x ≠ 1, the data is modeled by y = 4^x for x>1.
Therefore the curve is initially flat at x=1 but increases rapidly when x>1.

Answer:
The graph starts flat, but curves steeply upward.

Answer 2

Given the table representing a function.
x    1    2    3    4    5
y    1   16  64 256 1,024

As can be seen from the table, from the value of x = 2, the value of y is given by
$y=4^x$
i.e.
$4^2=16 \\ 4^3=64 \\ 4^4=256 \\ 4^5=1,024$
This represents an exponential function.

Therefore, the statement that would best describe the graph of the function is "The graph starts flat but curves steeply upward."