Question

Select the correct answer from each drop-downmenu.The function f is given by this table of values.

Answer 1

The parent function of the function represented in the table is exponential

If function f is vertically compressed by a factor of 1/4, the f(x) - values will be divided by 4.

A point in the table for the transformed function is (1, 6)

Step-by-step explanation:

The x values are increasing by 1 unit at a time, but the f(x) is always half the value before, for example

96/2 = 48

48/2 = 24

24/2 = 12

12/2 = 6

This is the behavior of an exponential function and the equation that describes this table is:

`f(x)=96((1)/(2))^(x+1)`

Because

`\begin{gathered} f(-1)=96((1)/(2))^(-1+1)=96((1)/(2))^0=96 \\ f(0)=96((1)/(2))^(0+1)=96((1)/(2))^1=96((1)/(2))=48 \\ f(1)=96((1)/(2))^(1+1)=96((1)/(2))^2=96((1)/(4))=24 \\ f(2)=96((1)/(2))^(2+1)=96((1)/(2))^3=96((1)/(8))=12 \\ f(3)=96((1)/(2))^(3+1)=96((1)/(2))^4=96((1)/(16))=6 \end{gathered}`

Therefore, the parent function represented in the table is Exponential.

Then, to make a vertical compression by a factor of 1/4, we need to multiply the values of f(x) by 1/4. It is the same to divide the values of f(x) by 4.

So, if function f is vertically compressed by a factor of 1/4, the f(x) - values will be divided by 4.

Therefore, the equation for the vertical compressed function is:

`f(x)=(1)/(4)(96)((1)/(2))^(x+1)=24((1)/(2))^(x+1)`

So, we can verify that (1, 6) is a point in the transformed function by replacing x by 1 on the equation above.

`f(1)=24((1)/(2)_{})^(1+1)=24((1)/(2))^2=24((1)/(4))=6`

Then, a point in the table for the transformed function is (1, 6)