Chapter 2: Q. 92 (page 116)

Suppose $(1, 3)$ is a point on the graph of $y = f (x)$ .
(a) What point is on the graph of $y = f (x + 3) - 5$ ?
(b) What point is on the graph of $y = - 2 f (x - 2) + 1$ ?
(c) What point is on the graph of $y = (2 x + 3)$ ?

Short Answer

Expert verified

Part (a). The point $(- 2, - 2)$ is on the graph $y = f (x + 3) - 5$ .

Part (b). The point $(3, - 5)$ is on the graph $y = - 2 f (x - 2) + 1$ .

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

Step by step solution

Part (a) Step 1. Finding the point on y=f(x+3)-5

It is given that $(1, 3)$ is a point on the graph $y = f (x)$ .

So, substituting $x + 3 = 1$ in the function

$y = f (x + 3) - 5$ :

$x + 3 = 1 x = 1 - 3 x = - 2$

Now, we have:

$y = f (1) - 5 y = 3 - 5 [f (1) = 3] y = - 2$

Hence, $(- 2, - 2)$ is on the graph $y = f (x + 3) - 5$

Part (b) Step 1. Finding the point on y=-2f(x-2)+1

It is given that $(1, 3)$ is a point on the graph $y = f (x)$ .

So, substituting $x - 2 = 1$ in the function

$y = - 2 (x - 2) + 1$ :

$x - 2 = 1 x = 1 + 2 x = 3$

Now, we have:

$y = - 2 f (1) + 1 y = - 2 (3) + 1 y = - 6 + 1 y = - 5$

Hence, $(3, - 5)$ is on the graph $y = - 2 f (x - 2) + 1$

Part (c) Step 1. Finding the point on y=f2x+3

It is given that $(1, 3)$ is a point on the function $y = f (x)$ .

So, substituting $2 x + 3 = 1$ in the function $y = f (2 x + 3)$

$2 x + 3 = 1 2 x = 1 - 3 2 x = - 2 x = - 1$

Now, we have:

$y = f (1) y = 3 [f (1) = 3]$

Hence, $(- 1, 3)$ is on the graph $y = f (2 x + 3)$

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Suppose $(1, 3)$ is a point on the graph of $y = f (x)$ .
(a) What point is on the graph of $y = f (x + 3) - 5$ ?
(b) What point is on the graph of $y = - 2 f (x - 2) + 1$ ?
(c) What point is on the graph of $y = (2 x + 3)$ ?

Short Answer

Step by step solution

Part (a) Step 1. Finding the point on y=f(x+3)-5

Part (b) Step 1. Finding the point on y=-2f(x-2)+1

Part (c) Step 1. Finding the point on y=f2x+3

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Suppose 1,3is a point on the graph of y=f(x).(a) What point is on the graph ofy=f(x+3)-5?(b) What point is on the graph of y=-2fx-2+1?(c) What point is on the graph of y=2x+3?

Short Answer

Step by step solution

Part (a) Step 1. Finding the point on y=f(x+3)-5

Part (b) Step 1. Finding the point on y=-2f(x-2)+1

Part (c) Step 1. Finding the point on y=f2x+3

One App. One Place for Learning.

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Study anywhere. Anytime. Across all devices.

Suppose $(1, 3)$ is a point on the graph of $y = f (x)$ .
(a) What point is on the graph of $y = f (x + 3) - 5$ ?
(b) What point is on the graph of $y = - 2 f (x - 2) + 1$ ?
(c) What point is on the graph of $y = (2 x + 3)$ ?