QuestionGraph the functions $f(x)=\sqrt{x}$ and $g(x)$ for given $x$ values. Describe the relation between their graphs.

Studdy Solution

STEP 1

Assumptions1. We are given two functions, $f(x)$ and $g(x)$ , which are both square root functions. . We are given specific integer values of $x$ for each function.
3. We are asked to graph these functions and describe how the graph of $g$ is related to the graph of $f$ .
4. We are instructed to only graph the functions for values of $x$ that result in the expression under the square root sign being greater than or equal to zero.

STEP 2

For each function, we will first calculate the corresponding $y$ values using the given $x$ values.For $f(x)=\sqrt{x}$ and $x=0,1,4,9$ , we calculate $f(0)=\sqrt{0}=0$ $f(1)=\sqrt{1}=1$ $f(4)=\sqrt{4}=2$ $f(9)=\sqrt{9}=$

STEP 3

Next, for $g(x)=\sqrt{x}-1$ and $x=0,1,,9$ , we calculate $g(0)=\sqrt{0}-1=0-1=-1$ $g(1)=\sqrt{1}-1=1-1=0$ $g()=\sqrt{}-1=2-1=1$ $g(9)=\sqrt{9}-1=3-1=2$

STEP 4

Now, we plot the points for $f(x)$ and $g(x)$ on the same graph. The points for $f(x)$ are $(0,0)$ , $(1,1)$ , $(4,2)$ , and $(9,3)$ . The points for $g(x)$ are $(0,-1)$ , $(1,0)$ , $(4,1)$ , and $(9,2)$ .

STEP 5

By observing the graph, we can see that the graph of $g(x)$ is a vertical translation of the graph of $f(x)$ one unit down. This is because $g(x)=\sqrt{x}-1$ is the same as $f(x)=\sqrt{x}$ but subtracted by1.

STEP 6

Repeat steps2-5 for the remaining exercises, replacing $f(x)$ and $g(x)$ with the given functions and using the given $x$ values.

STEP 7

For exercise52, $f(x)=\sqrt{x}$ and $g(x)=\sqrt{x}+2$ , we find that the graph of $g(x)$ is a vertical translation of the graph of $f(x)$ two units up.

STEP 8

For exercise53, $f(x)=\sqrt{x}$ and $g(x)=\sqrt{x-1}$ , we find that the graph of $g(x)$ is a horizontal translation of the graph of $f(x)$ one unit to the right.

STEP 9

For exercise54, $f(x)=\sqrt{x}$ and $g(x)=\sqrt{x+2}$ , we find that the graph of $g(x)$ is a horizontal translation of the graph of $f(x)$ two units to the left.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms