Chapter 2: Q. 93 (page 116)

Suppose $(- 3, 5)$ is a point on the graph of role="math" localid="1646038713489" $y = g (x)$ .
(a) What point is on the graph of role="math" localid="1646038862365" $y = g (x + 1) - 3$ ?
(b) What point is on the graph of $y = - 3 g (x - 4) + 3$ ?
(c) What point is on the graph of $y = g (3 x + 9)$ ?

Short Answer

Expert verified

Part (a). The point $(- 4, 2)$ is on the graph $y = g (x + 1) - 3$ .

Part (b). The point $(1, - 12)$ is on the graph $y = - 3 g (x - 4) + 3$ .

Part (c). The point $(- 4, 5)$ is on the graph $y = g (3 x + 9)$ .

Step by step solution

Part (a) Step 1. Finding the point on y=g(x+1)-3

It is given that $(- 3, 5)$ is a point on the graph $y = g (x)$ .

So, substituting $x + 1 = - 3$ in the functionlocalid="1646040741825" $y = g (x + 1) - 3$ :

$x + 1 = - 3 x = - 3 - 1 x = - 4$

Now, we have:

$y = g (- 3) - 3 y = 5 - 3 [g (- 3) = 5] y = 2$

Hence, $(- 3, 5)$ is on the graph $y = g (x + 1) - 3$

Part (b). Step 1. Finding the point on the graph y=-3gx-4+3

It is given that $(- 3, 5)$ is a point on the graph $y = g (x)$ .

So, substituting $x - 4 = - 3$ in the function $y = - 3 g (x - 4) + 3$ :

$x - 4 = - 3 x = - 3 + 4 x = 1$

Now , we have:

$y = - 3 g (- 3) + 3 y - 3 \times 5 + 3 y = - 12$

Hence, $(1, - 12)$ is on the graph $y = - 3 g (x - 4) + 3$

Part (c) Step 1. Finding the point on the graph y=g(3x+9)

It is given that $(- 3, 5)$ is a point on the graph $y = g (3 x + 9)$ .

Substituting $3 x + 9 = - 3$ in the function $y = g (3 x + 9)$ :

$3 x + 9 = - 3 3 x = 3 + 9 3 x = 12 x = 4$

Now, we have:

$y = g (- 3) y = 5$

Hence, $(- 4, 5)$ is on the graph

y = g (3 x + 9)

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Short Answer

Step by step solution

Part (a) Step 1. Finding the point on y=g(x+1)-3

Part (b). Step 1. Finding the point on the graph y=-3gx-4+3

Part (c) Step 1. Finding the point on the graph y=g(3x+9)

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Suppose -3,5is a point on the graph of role="math" localid="1646038713489" y=g(x).(a) What point is on the graph of role="math" localid="1646038862365" y=g(x+1)-3?(b) What point is on the graph of y=-3gx-4+3?(c) What point is on the graph ofy=g3x+9?

Short Answer

Step by step solution

Part (a) Step 1. Finding the point on y=g(x+1)-3

Part (b). Step 1. Finding the point on the graph y=-3gx-4+3

Part (c) Step 1. Finding the point on the graph y=g(3x+9)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Statistics

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.