Chapter 2: Q. 33 (page 113)

If $(1, 3)$ is a point on the graph of $y = f (x)$ , which of the following points must be on the graph of $y = 2 f (x)$ ?

Short Answer

Expert verified

The point $(1, 6)$ lies on the graph of $y = 2 f (x)$ so the optionc is correct

Step by step solution

Step 1. Given data

The point $(1, 3)$ lies on the graph of the function $y = f (x)$

transformed function is $y = 2 f (x)$

Step 2. Explanation of correct option C

Point $(1, 3)$ lies on $y = f (x)$

so $f (1) = 3$

$y = 2 f (x)$ is obtained by stretching $y = f (x)$ vertically

so y coordinate of $y = 2 f (x)$ at $x = 1$

$y = 2 f (x) y = 2 f (1) y = 2 (3) y = 6$

point $(1, 6)$ lies on $y = 2 f (x)$ so option cis correct.

Step 3. explanation of incorrect options

y coordinate of $y = 2 f (x)$ is two times of $y = f (x)$ so point $(1, \frac{3}{2})$ can not lie on it
y coordinate of $y = 2 f (x)$ is two times of $y = f (x)$ so point $(2, 3)$ can not lie on it
y coordinate of $y = 2 f (x)$ is two times of $y = f (x)$ so point $(\frac{1}{2}, 3)$ can not lie on it

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If $(1, 3)$ is a point on the graph of $y = f (x)$ , which of the following points must be on the graph of $y = 2 f (x)$ ?

Short Answer

Step by step solution

Step 1. Given data

Step 2. Explanation of correct option C

Step 3. explanation of incorrect options

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If (1,3)is a point on the graph of y=f(x), which of the following points must be on the graph ofy=2f(x)?

Short Answer

Step by step solution

Step 1. Given data

Step 2. Explanation of correct option C

Step 3. explanation of incorrect options

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

If $(1, 3)$ is a point on the graph of $y = f (x)$ , which of the following points must be on the graph of $y = 2 f (x)$ ?