Question

Using the function f(x)=1/4x^2and the values x = {-4-2, 0, 2, }, complete the table below

Answer 1

You have to determine the ordered pairs for given values of x of the function:

`f(x)=(1)/(4)(x)^2`

To do so, replace the function with each value of x and calculate the corresponding value of f(x):

1) For x=-4

-Replace the value in the formula

`\begin{gathered} f(x)=(1)/(4)(x)^2 \\ f(-4)=(1)/(4)(-4)^2 \end{gathered}`

-First solve the exponent

`f(-4)=(1)/(4)\cdot16`

-Then solve the multiplication

`f(-4)=4`

The first ordered pair is (-4,4)

2) For x=-2

-Replace the value in the formula

`\begin{gathered} f(x)=(1)/(4)(x)^2 \\ f(-2)=(1)/(4)(-2)^2 \end{gathered}`

-First solve the exponent

`f(-2)=(1)/(4)\cdot4`

-Then solve the multiplication

`f(-2)=1`

The second ordered pair is (-2,1)

3) For x=0

-Replace the value in the formula

`\begin{gathered} f(x)=(1)/(4)(x)^2 \\ f(0)=(1)/(4)(0)^2 \end{gathered}`

-First solve the exponent

`f(0)=(1)/(4)\cdot0`

-Then solve the multiplication

`f(0)=0`

The third ordered pair is (0,0)

4) Fox x=2

-Replace the value in the formula

`\begin{gathered} f(x)=(1)/(4)(x)^2 \\ f(2)=(1)/(4)(2)^2 \end{gathered}`

-First solve the exponent

`f(2)=(1)/(4)\cdot4`

-Then solve the multiplication

`f(2)=1`

The fourth ordered pair is (2,1)

5) For x=4

-Replace the value in the formula

`\begin{gathered} f(x)=(1)/(4)(x)^2 \\ f(4)=(1)/(4)(4)^2 \\ \end{gathered}`

-First solve the exponent

`f(4)=(1)/(4)\cdot16`

-Then solve the multiplication

`f(4)=4`

The fifth ordered pair is (4,4)