Chapter 2: Q. 7 (page 126)

Consider the function
$g (x) = \{\begin{cases} 2 x + 1 & i f x < - 1 \\ x - 4 & i f x \geq - 1 \end{cases}$
(a) Graph the function.
(b) List the intercepts.
(c) Find $g (- 5)$ .
(d) Find $g (2)$ .

Short Answer

Expert verified

(a) Graph of function is

(b) the x-intercept is $(4, 0)$ and the y-intercept is $(0, - 4)$

(d) value of $g (2)$ is $- 2$

Step by step solution

Step 1. given data

The given function is

$g (x) = \{\begin{cases} 2 x + 1 & i f x < - 1 \\ x - 4 & i f x \geq - 1 \end{cases}$

Step 2. Part (a)

Determine the different points for the graph of the function $g (x) = 2 x + 1$ for which $x < - 1$

Determine the different points for the graph of the function $g (x) = x - 4$ for which $x > = - 1$

Step 2. graph of the function

Plot points and connect them through a straight line for the graph of functions

Step 4. Part (b)

For thex-intercept, $y = 0$

then x value of $g (x) = x - 4$ when $g (x) = 0$ is

$g (x) = x - 4 0 = x - 4 x = 4$

so x-intercept is $(4, 0)$

For they-intercept,

x = 0

soyvalue of

g (x) = x - 4

$g (x) = x - 4 g (x) = 0 - 4 g (x) = - 4 y = - 4$

y-intercept is $(0, - 4)$

Step 5. Part (c)

$x = - 5$ is less than $- 1$ , so the function will be $g (x) = 2 x + 1$

substitute $- 5$ for x in the function

$g (x) = 2 x + 1 g (- 5) = 2 (- 5) + 1 g (- 5) = - 10 + 1 g (- 5) = - 9$

Step 6. Part (d)

$x = 2$ is greater than $- 1$ so function will be $g (x) = x - 4$

substitute $2$ forxin the function

$g (x) = x - 4 g (2) = 2 - 4 g (2) = - 2$

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Consider the function
$g (x) = \{\begin{cases} 2 x + 1 & i f x < - 1 \\ x - 4 & i f x \geq - 1 \end{cases}$
(a) Graph the function.
(b) List the intercepts.
(c) Find $g (- 5)$ .
(d) Find $g (2)$ .

Short Answer

Step by step solution

Step 1. given data

Step 2. Part (a)

Step 2. graph of the function

Step 4. Part (b)

Step 5. Part (c)

Step 6. Part (d)

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Consider the functiong(x)=2x+1ifx<-1x-4ifx≥-1(a) Graph the function.(b) List the intercepts.(c) Find g(-5).(d) Find g(2).

Short Answer

Step by step solution

Step 1. given data

Step 2. Part (a)

Step 2. graph of the function

Step 4. Part (b)

Step 5. Part (c)

Step 6. Part (d)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Consider the function
$g (x) = \{\begin{cases} 2 x + 1 & i f x < - 1 \\ x - 4 & i f x \geq - 1 \end{cases}$
(a) Graph the function.
(b) List the intercepts.
(c) Find $g (- 5)$ .
(d) Find $g (2)$ .