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Big Ideas Math Algebra 2, 2014

BI

Big Ideas Math Algebra 2, 2014 View details

2. Transformations of Linear and Absolute Value Functions

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Exercise 38 Page 18

How can we move the graph of $f$ to get the graph of $g ?$ Do you remember the formula for the area of the triangle?

Transformation: A vertical translation $5$ units up.
Area of the Triangle: $9$

Practice makes perfect

First, we will take a look at the given graph and describe the transformation. Then we are going to recall the formula of the area of a triangle to find the area of the shaded figure.

Transformation

Let's look at the given graph, focusing only on the given functions.

As we can see, the graph of $f$ is shifted $5$ units up. This is a vertical translation.

Area of the triangle

Now let's recall the formula for the area of the triangle.

A = \frac{1}{2} b h

In this formula,

b

is the base and

h

is the height of the triangle. To find these values, let's look at the given graphs once again.

The base of this triangle is

6

and the height equals

3 .

Now we will substitute these values into the formula to find the area.

A = \frac{1}{2} b h

$b = 6$ , $h = 3$

A = \frac{1}{2} (6) (3)

▼

Simplify right-hand side

Multiply

A = \frac{1}{2} (18)

MoveLeftFacToNumOne

$a \cdot \frac{1}{b} = \frac{a}{b}$

A = \frac{1 8}{2}

Calculate quotient

A = 9

The area of the shaded triangle is

9 .

Subchapter links

Communicate Your Answer p.11

Monitoring Progress p.13-15

Exercises p.16-18