Chapter 5: Q.95 (page 316)

(a) Graph $f (x) = 2^{x} - 4$ f
(b) Find the zero of f.
(c) Based on the graph, solve $f (x) < 0$ .

Short Answer

Expert verified

a) The graph of the function is

b) The zero of the function is $x = 2$

c) The value of $f (x) < 0$ is when $x < 2$

Step by step solution

Given information

We are given a function $f (x) = 2^{x} - 4$

Part a) Step 1: Create a table to plot the graph of function

We get,

x	$f (x) = 2^{x} - 4$
-1	$- \frac{7}{2}$
0	-3
1	-2
2	0
3	4

The graph of the function is

Part b) Step 1: Solve for f(x)=0

We get,

$f (x) = 0 2^{x} - 4 = 0 2^{x} = 4 2^{x} = 2^{2} x = 2$

$x = 2$ is the zero of the function.

Part c) Step 1: Solve for f(x)<0

From the graph the zero of the function is at $(2, 0)$ ,hence $f (x) < 0 f o r x < 2$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

(a) Graph $f (x) = 2^{x} - 4$ f
(b) Find the zero of f.
(c) Based on the graph, solve $f (x) < 0$ .

Short Answer

Step by step solution

Given information

Part a) Step 1: Create a table to plot the graph of function

Part b) Step 1: Solve for f(x)=0

Part c) Step 1: Solve for f(x)<0

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Pure Maths

Decision Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

(a) Graphf(x)=2x-4 f(b) Find the zero of f.(c) Based on the graph, solve f(x)<0.

Short Answer

Step by step solution

Given information

Part a) Step 1: Create a table to plot the graph of function

Part b) Step 1: Solve for f(x)=0

Part c) Step 1: Solve for f(x)<0

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Pure Maths

Decision Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

(a) Graph $f (x) = 2^{x} - 4$ f
(b) Find the zero of f.
(c) Based on the graph, solve $f (x) < 0$ .