Question

what is the equation of the function shown in the graph, given the equation of the parent function is f (x) =1.5x

Answer 1

Any number raised to the power of 0 is 1.

So 1.5^x where x = 0 gives you f(0) = 1

That means that the original function should have a y-value of 1 when x is 0.

Since the new graph has a y-value of -3 at x = 0, then the new graph is simply f(x) shifted down 4 units

Answer 2

4.
`g(x)=(1.5)^x-4`

Explanation:

We are given that a graph of the function in the figure.

The equation of parent function

`f(x)=1.5^x`

We have to find the equation of graph of the function shown in the figure.

The given graph cuts the y- axis at point (0,-3).

The given graph passing through the point (2,-1.75).

1.
`g(x)=1.5^x-2`

Substitute x=0

`g(0)=(1.5)^0-2=1-2=-1`

The graph cut the y- axis at the point (0,-1).

Therefore, it is not an equation given graph.

2.
`g(x)=(1.5)^x-3`

Substitute x=0

`g(0)=(1.5)^0-3=1-3=-2`

The graph cut the y- axis at the point (0,-2).

Therefore, it is not an equation given graph.

3.
`g(x)=(1.5)^x+2`

Substitute x=0

`g(0)=(1.5)^0+2=1+2=3`

The graph cut the y- axis at the point (0,3).

Therefore, it is not an equation given graph.

4.
`g(x)=(1.5)^x-4`

Substitute x=0

`g(0)=(1.5)^0-4=1-4=-3`

The graph cut the y- axis at the point (0,-3).

Substitute x=2

`g(2)=(1.5)^2-4=-1.75`

The graph passing through the point (2,-1.75).

Hence, it is an equation of given graph.