Question

Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.

Answer 1

D. y-intercept = 5

Explanation:

I majored in Mathematics

Answer 2

ANSWER

The graph in option D.

The y-intercept is

`5`

EXPLANATION.

The given function is


`f(x) = 5( {2}^(x) )`

This function is of the form


`f(x) = a( {b}^(kx) ).`
Since

`k > 0`
the graph of this function will approach positive infinity as the values of x increases without bounds.

This means the graph of this function rises dramatically as the values of x becomes bigger and bigger.

While the graph approaches zero for infinitely smaller values of x. This means that, the graph is asymptotic to the negative x-axis.

For the y-intercept of this graph, we put

`x = 0`
into the function to obtain,


`f(0)=5( {2}^(0) )`

This will give us,


`f(0)=5( 1 )=5`

Therefore the correct answer is D.