Math  /  Geometry

Question```latex \text{Use the graph to determine the following.} \begin{enumerate} \item the function's domain \item the function's range \item the xx-intercepts, if any \item the yy-intercept, if any \item the function values f(2)f(-2) and f(0)f(0) \end{enumerate}
\text{Assume that the graph of the function continues its trend beyond the displayed coordinate grid.} ```

Studdy Solution

STEP 1

What is this asking? We're looking at a graph and figuring out some key things about it, like where it lives on the x and y-axes, where it crosses those axes, and what its value is at certain points! Watch out! Don't mix up domain and range, and be careful when reading values from the graph!

STEP 2

1. Find the Domain
2. Find the Range
3. Find the x-intercepts
4. Find the y-intercept
5. Calculate f(2)f(-2) and f(0)f(0)

STEP 3

The **domain** is all the possible xx values the graph can have.
Since the graph continues its trend beyond the grid, it goes on forever to the left and forever to the right.

STEP 4

That means the domain is all real numbers!
We can write that fancy-style as (,)(-\infty, \infty).

STEP 5

The **range** is all the possible yy values.
This graph has a lowest point, and then goes up forever.

STEP 6

The lowest point looks like it's at y=4y = -4.
So, the range is everything from 4-4 up to infinity, which we write as [4,)[-4, \infty).
Remember the square bracket means 4-4 is included!

STEP 7

The **xx-intercepts** are where the graph crosses the xx-axis.
This happens when y=0y = 0.

STEP 8

Looking at the graph, it crosses the xx-axis at x=1x = -1 and x=1x = 1.
So, the xx-intercepts are (1,0)(-1, 0) and (1,0)(1, 0).

STEP 9

The **yy-intercept** is where the graph crosses the yy-axis.
This happens when x=0x = 0.

STEP 10

The graph crosses the yy-axis at y=3y = -3.
So, the yy-intercept is (0,3)(0, -3).

STEP 11

f(2)f(-2) means "the value of the function when x=2x = -2".
We find 2-2 on the xx-axis and look up to see where the graph is.

STEP 12

It looks like the graph is at y=1y = 1 when x=2x = -2.
So, f(2)=1f(-2) = 1.

STEP 13

Now, let's find f(0)f(0).
This means "the value of the function when x=0x = 0".

STEP 14

We already found this when we were looking for the yy-intercept! f(0)=3f(0) = -3.

STEP 15

Domain: (,)(-\infty, \infty) Range: [4,)[-4, \infty) xx-intercepts: (1,0)(-1, 0) and (1,0)(1, 0) yy-intercept: (0,3)(0, -3) f(2)=1f(-2) = 1 f(0)=3f(0) = -3

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