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Chapter 8: Q. 8 (page 556)

Sketch the graph of each of the following functions:
$(a) y = x$
$(b) y = x^{2} (c) y = \sqrt{x} (d) y = x^{3} (e) y = e^{x} (f) y = \ln x (g) y = \sin x (h) y = \cos x (i) y = \tan x$

Short Answer

Expert verified

The required graphs

(a)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Step by step solution

01

Part (a) Step 1. Given Information

A function is given as $y = x$

We need to plot the given function on a graph.

02

Part (b) Step 2. Required graph

Points on the graph are:

$(0, 0), (1, 1), (2, 2), (3, 3)$

Plotting these points we get the graph as,

03

Part (b) Step 1. Required graph

The function is $y = x^{2}$

Points are:

$(1, 1), (2, 4), (3, 9), (- 2, 4), (- 3, 9), (- 1, 1)$

Plotting these points, we get the graph as,

04

Part (c) Required Graph

The function is $y = \sqrt{x}$

Points are $(1, 1), (4, 2), (9, 3)$

The graph will be:

05

Part (d) Required graph

The function is $y = x^{3}$

The points to be plotted on the graph are

$(1, 1), (2, 8), (- 2, - 8), (- 1, - 1)$

06

Part (e) Required Graph

The function is $y = e^{x}$

Points to be plotted are:

$(- 2, 0.135) (1, 2.718) (0, 1)$

07

Part (f) Required Graph

The function is $y = \ln x$

The graph of the function is

08

Part (g) Step 1. Required Graph

The function is $y = \sin x$

The graph will be

09

Part (h) Step 1. Required Graph

The function is $y = \cos x$

The graph will be

10

Part (i) Step 1. Required Graph

The function is $y = \tan x$

The graph will be

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Most popular questions from this chapter

A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall?

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