Question

Graph the inequality :
$x \geqslant 1 \\ y = 4x - 2$
and also define domain and range of
$y ^2 = x - 2$
​

Answer 1

Answer: The graph of the inequality and line are attached.

The domain of the function is $[2,$∞$]$  and range is $[0,$∞$]$

Step-by-step explanation:

Tip

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

Explanation

Given -

Inequality $x\geq 1$ and $y =4x-2$

Function $y^{2} =x-2$

To find-

Graph of the inequality

Domain and range of the function

Approach-

To graph any inequality we need to shade the area that will satisfy the inequality

To find domain we will see what values x can have and to find the range we will se what values y will have.

Step

Step 1 of3

Draw a straight line through $x=1$ and shade the area towards the right

Step 2 of3

To plot $y=4x-2$ , first keep $y=0$ so you get $x=\frac{1}{2}$  so the coordinate will be$(\frac{1}{2}, 0)$ now keep $x=0$ we get $y=-2$ so the coordinate $(0,-2)$ .Now join both the points you will get the desired line.

Step 3 of3

$y^{2}=x-2\\y=\sqrt{x-2}$

for domain $x-2\geq 0\\x\geq 2$

so domain will be$[2,$∞$]$  

for range we know square root of a positive number will be positive so range will be$[0,$∞$]$

Final answer

The graph of the inequality and line are attached.

The domain of the function is $[2,$∞$]$  and range is $[0,$∞$]$