Question

the graph of y= sqrtx is translated 4 units left and 1 unit up to create the function h(x). the graph of h(x) is shown on the coordinate grid. what is the range of h(x)?

Answer 1

Answer:

The range of the function h(x) is $R=\{y|y\geq 1\}$

Step-by-step explanation:

Given : The graph of $y=\sqrt{x}$ is translated 4 units left and 1 unit up to create the function h(x).

To find : What is the range of h(x)?

Solution :

When the graph f(x) is translated then

1) f(x)+b shifts the function b units upward.

2) f(x + b) shifts the function b units to the left.

The graph of $y=\sqrt{x}$ is translated 4 units left.

i.e. $y=\sqrt{x+4}$

The graph of $y=\sqrt{x}$ is translated 1 unit up.

i.e. $y=\sqrt{x+4}+1$

So, The required function h(x) is $h(x)=\sqrt{x+4}+1$

The range of a function is set of output values produce by a function.

In the given graph, y value is always greater than and equal to 1.

So, The range of the function h(x) is $R=\{y|y\geq 1\}$

Answer 2

Answer:

C. $\{y|y\ge 1\}.$

Step-by-step explanation:

Consider the parent function $f(x)=\sqrt{x}.$

• The domain of this function is $x\ge 0;$
• The range of this function is $y\ge 0.$

Now consider given function $h(x)=\sqrt{x+4}+1$ (translated 4 units left and 1 unit up.)

• The domain of this function is $x\ge -4;$
• The range of this function is $y\ge 1.$