Question

Which of the following is true about the graph of (x)=7^x?

A)It intercepts the x-axis
B)It intercepts both axis
C)It intercepts neither axis
D)It intercepts the y-axis

Answer 1

it only intercepts the y acis but it gets extremely close to the x axis. it never touches or crosses the x axis. D

Answer 2

D)It intercepts the y-axis

Explanation:

The given function is
`f(x)=7^x`

In order to check that the given graph intersects which of the two axes , we find the x and y intercepts.

For y - intercept, x =0

`f(x)=7^0`

Any number with power 0 is 1. Hence, we have

`f(x)=1`

Hence, the y- intercept is 1 and the graph intersects the y axis at the point (0,1)

Now, we find x- intercept

For x - intercept, y =0

`0=7^x`

For no value of x, the value of the function equal to zero.

Hence, no real values of x.

Thus, the graph doesn't intersect the x axis.

Therefore, the correct option is D.