Question

Express the function graphed on the axes below as a piecewise function.10-8-61

Answer 1

y = 1, where x ≤ -3

y = 1.5x + 2, where x > 2

`f(x)=\begin{cases}1\text{ for when x }\le-3 \\ 1.5x+2\text{ for when x > 2}\end{cases}`

Step-by-step explanation

For a piecewise function, it means the graph will have different values at different values of x.

In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow line is usually unshaded.

But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow line will be shaded.

So, starting the piecewise function with the left side of the graph.

y = 1, where x ≤ -3

Then, for the right hand side, it is a straight line that we will find its equation using two points on the line. We will write its equation without the inequality sign first.

Two points on the line include (2, 5) and (4, 8)

Equation of a line has the general form of y = mx + b

(2, 5)

x = 2, y = 5

5 = 2m + b

(4, 8)

x = 4, y = 8

8 = 4m + b

Writing the two equatios together,

2m + b = 5

4m + b = 8

Subtract equation 2 from equation 1

4m - 2m + b - b = 8 - 5

2m = 3

Divide both sides by 2

(2m/2) = (3/2)

m = (3/2)

2m + b = 5

2 (3/2) + b = 5

3 + b = 5

b = 5 - 3 = 2

So, the normal equation of the line is y = (3x/2) + 2 OR y = 1.5x + 2

Now to write it in piecewise form, we can see that the beginning of the arrowline is an unshaded circle.

So,

y = 1.5x + 2, where x > 2

We can write the entire piecewise functions for the graph as

y = 1, where x ≤ -3

y = 1.5x + 2, where x > 2

Hope this Helps!!!