# Evaluate Functions

#### How do you evaluate functions?

The same way that you substitute values into equations!

Example 1

What is the value of $$x$$ given the equation $$y = 2x$$ when $$x = 5$$?

Substitute '5' in for x :

The one new aspect of function notation is the emphasis on input and output .

Example 2

What is the value of $$x$$ given the equation $$y = x-5$$ when $$x = 7$$?

Substitute '7' in for x :

### Practice Problems

##### Problem 1
Step 1

Identify all of the occurrences of 'x' and substitute the input in

$$k(\blue{x }) =3 \blue{x } \\ k(\blue{5 }) =3\cdot \blue{5 }$$

Step 2

Compute result.

$$k(\blue5 ) =3\cdot \blue 5 \\ = \red {15}$$

$$k(\blue {input }) =\red {output} \\ k(\blue 5) =\red {15}$$

##### Problem 2
Step 1

Identify all of the occurrences of 'x' and substitute the input in

$$g(\blue x ) =3 \blue x ^2 + 7 \blue x \\ g(\blue 4 ) =3\cdot \blue 4 ^2 + 7\cdot \blue 4$$

Step 2

Compute result.

$$g(\blue 4 ) =3\cdot \blue 4 ^2 + 7\cdot \blue 4 \\ g(\blue 4 ) = \red{76}$$

$$g(\blue {input }) =\red {output} \\ g(\blue 4) =\red {76}$$

##### Problem 3
Step 1

Identify all of the occurrences of 'x' and substitute the input in

$$h(\blue x ) = \sqrt{\blue x ^3 -4}-| \blue{x }| \\ h(\blue {5 }) = \sqrt{\blue 5 ^3 - 4 } - | \blue 5 |$$

Step 2

Compute result.

$$h(\blue 5 ) = \sqrt{\blue 5 ^3 -4}-|\blue 5 | \\ h(\blue 5 ) =50 \\ h(\blue 5) = \red 6$$

$$h(\blue {input }) =\red {output} \\ h(\blue 5) =\red 6$$

##### Problem 4
Step 1

Identify all of the occurrences of 'x' and substitute the input in

$$f(\blue x ) = -3 \blue x ^2 + 5\blue x - 1 \\ f(\blue 6 ) = -3 \cdot \blue 6 ^2 + 5\cdot \blue 6 - 1$$

Step 2

Compute result.

$$f(\blue 6 ) = -3 \cdot \blue 6^2 + 5\cdot \blue 6 - 1 \\ f(\blue 6) = \red{-79}$$

$$f(\blue {input }) =\red {output} \\ f(\blue 6) =\red {-79}$$

##### Problem 5
Step 1

Identify all of the occurrences of 'x' and substitute the input in

$$h(\blue t ) = -5\blue t^2 + 40 \blue t + 1.2 \\ h(\blue 4 ) = -5 \cdot \blue 4 ^2 + 40 \cdot \blue 4 + 1.2$$

Step 2

Compute result.

$$h(\blue 4 ) = -5 \cdot \blue 4^2 + 40 \cdot \blue 4 + 1.2 \\ h(\blue 4 ) = \red{81.2}$$

$$h(\blue {input }) =\red {output} \\ h(\blue 4) =\red {81.2}$$

Here is a picture of graph of projectile's path with the point $$(\blue {t}, \red{h(t)}) (\blue 4, \red {81.2})$$ :

##### Problem 6
Step 1

Identify all of the occurrences of 'x' and substitute the input in

$$h(\blue t) = 250 (0.5)^{ \frac{\blue t}{25} } \\ h(\blue { 98 }) = 250 (0.5)^{ \frac{\blue{98}}{25} }$$

Step 2

Compute result.

$$h(\blue{98}) = 250 (0.5)^{ \frac{\blue{98}}{25} } \\ h(\blue{98}) = \red{16.5159}$$

$$h(\blue {input }) =\red {output} \\ h(\blue {98}) =\red {16.5159}$$

Here is a picture of graph of projectile's path with the point $$(\color{blue} {t}, \color{red} {h(t)}) (\color{blue} {98} , \color{red} {16.5159})$$ :.

Graph generated by Meta Calculator's graphing calc