Question

Sketch the graph of each of the following functions:

$\text{(a)}y=x$

$$\begin{gathered} \text{(b)}y=x^2 \\ \text{(c)}y=\sqrt{x} \\ \text{(d)}y=x^3 \\ \text{(e)}y=e^x \\ \text{(f)}y=\ln x \\ \text{(g)}y=\sin x \\ \text{(h)}y=\cos x \\ \text{(i)}y=\tan x \end{gathered}$$

Short answer

The required graphs

(a)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Step-by-step solution

Part (a) Step 1. Given Information

A function is given as $y=x$

We need to plot the given function on a graph.

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,

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,

Part (c) Required Graph

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

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

The graph will be:

Part (d) Required graph

The function is$y=x^3$

The points to be plotted on the graph are

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

Part (e) Required Graph

The function is$y=e^x$

Points to be plotted are:

$$\begin{gathered} (-2,0.135) \\ (1,2.718) \\ (0,1) \end{gathered}$$

Part (f) Required Graph

The function is$y=\ln x$

The graph of the function is

Part (g) Step 1. Required Graph

The function is$y=\sin x$

The graph will be

Part (h) Step 1. Required Graph

The function is$y=\cos x$

The graph will be

Part (i) Step 1. Required Graph

The function is$y=\tan x$

The graph will be