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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)?

the graph of y sqrtx is translated 4 units left and 1 unit up to create the function hx the graph of hx is shown on the coordinate grid what is the range of hx class=

Respuesta :

frika

Answer:

C. [tex]\{y|y\ge 1\}.[/tex]

Step-by-step explanation:

Consider the parent function [tex]f(x)=\sqrt{x}.[/tex]

  • The domain of this function is [tex]x\ge 0;[/tex]
  • The range of this function is [tex]y\ge 0.[/tex]

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

  • The domain of this function is [tex]x\ge -4;[/tex]
  • The range of this function is [tex]y\ge 1.[/tex]

Answer:

The range of the function h(x) is [tex]R=\{y|y\geq 1\}[/tex]

Step-by-step explanation:

Given : The graph of [tex]y=\sqrt{x}[/tex] 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 [tex]y=\sqrt{x}[/tex] is translated 4 units left.

i.e. [tex]y=\sqrt{x+4}[/tex]

The graph of [tex]y=\sqrt{x}[/tex] is translated 1 unit up.

i.e. [tex]y=\sqrt{x+4}+1[/tex]

So, The required function h(x) is [tex]h(x)=\sqrt{x+4}+1[/tex]

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 [tex]R=\{y|y\geq 1\}[/tex]

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