Math / Algebra

QuestionUse the graph to determine $\mathbf{a}$ . the function's domain; b. the function's range; $\mathbf{c}$ . the x -intercepts, if any; $\mathbf{d}$ . the $y$ -intercept, if there is one; $\boldsymbol{e}$ . the following function values. $\begin{array}{l} f(-3) \\ f(2) \end{array}$ a. What is the domain? $(-\infty, \infty)$ (Type your answer in interval notation.) b. What is the range? $(-\infty,-3]$ (Type your answer in interval notation.) c. Enter the x-intercept(s). Select the correct choice below and fill in any answer boxes within your choice. A. The $x$ -intercept(s) is(are) $\square$ 1. (Type an integer. Use a comma to separate answers as needed.) B. There is no $x$ -intercept. d. Enter the $y$ -intercept. Select the correct choice below and fill in any answer boxes within your choice. A. The $y$ -intercept is $\square$ . (Type an integer.) B. There is no $y$ -intercept.

Studdy Solution

STEP 1

What is this asking? We're looking at a graph and figuring out the domain, range, x-intercept, y-intercept, and the value of the function at $f(-3)$ and $f(2)$ . Watch out! Don't mix up domain and range!
Domain is about the x-values and range is about the y-values!
Also, be careful when reading values from the graph!

STEP 2

1. Find the Domain
2. Find the Range
3. Find the x-intercept(s)
4. Find the y-intercept
5. Calculate $f(-3)$
6. Calculate $f(2)$

STEP 3

The domain is all the possible x-values the graph can have.
Looking at our graph, it keeps going to the left and right forever!

STEP 4

So, the domain is all real numbers, which we write as $(-\infty, \infty)$ in interval notation.

STEP 5

The range is all possible y-values.
The graph goes up forever from $-3$ , but it never goes lower than $-3$ .

STEP 6

So, the range is from negative infinity up to and including $-3$ .
In interval notation, that's $(-\infty, -3]$ .
Notice the square bracket because $-3$ is included!

STEP 7

The x-intercept is where the graph crosses the x-axis.
That happens when $y = 0$ .

STEP 8

Looking at our graph, it crosses the x-axis at $x = 3$ .
So, the x-intercept is 3.

STEP 9

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

STEP 10

Our graph crosses the y-axis at $y = -3$ .
So, the y-intercept is -3.

STEP 11

$f(-3)$ means we want to find the y-value when $x = -3$ .

STEP 12

Looking at the graph, when $x = -3$ , it looks like $y = -6$ .
So, $f(-3) = -6$ .

STEP 13

$f(2)$ means we're looking for the y-value when $x = 2$ .

STEP 14

From the graph, when $x = 2$ , it seems like $y = -4$ .
Therefore, $f(2) = -4$ .

STEP 15

* Domain: $(-\infty, \infty)$ * Range: $(-\infty, -3]$ * x-intercept: $3$ * y-intercept: $-3$ * $f(-3) = -6$ * $f(2) = -4$

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Studdy Solution

STEP 1

STEP 2

1. Find the Domain
2. Find the Range
3. Find the x-intercept(s)
4. Find the y-intercept
5. Calculate $f(-3)$
6. Calculate $f(2)$

STEP 3

The domain is all the possible x-values the graph can have.
Looking at our graph, it keeps going to the left and right forever!

STEP 4

So, the domain is all real numbers, which we write as $(-\infty, \infty)$ in interval notation.

STEP 5

The range is all possible y-values.
The graph goes up forever from $-3$ , but it never goes lower than $-3$ .

STEP 6

So, the range is from negative infinity up to and including $-3$ .
In interval notation, that's $(-\infty, -3]$ .
Notice the square bracket because $-3$ is included!

STEP 7

The x-intercept is where the graph crosses the x-axis.
That happens when $y = 0$ .

STEP 8

Looking at our graph, it crosses the x-axis at $x = 3$ .
So, the x-intercept is 3.

STEP 9

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

STEP 10

Our graph crosses the y-axis at $y = -3$ .
So, the y-intercept is -3.

STEP 11

$f(-3)$ means we want to find the y-value when $x = -3$ .

STEP 12

Looking at the graph, when $x = -3$ , it looks like $y = -6$ .
So, $f(-3) = -6$ .

STEP 13

$f(2)$ means we're looking for the y-value when $x = 2$ .

STEP 14

From the graph, when $x = 2$ , it seems like $y = -4$ .
Therefore, $f(2) = -4$ .

STEP 15

* Domain: $(-\infty, \infty)$ * Range: $(-\infty, -3]$ * x-intercept: $3$ * y-intercept: $-3$ * $f(-3) = -6$ * $f(2) = -4$

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Studdy Solution

STEP 1

STEP 2

1. Find the Domain2. Find the Range3. Find the x-intercept(s)4. Find the y-intercept5. Calculate f(−3)f(-3)f(−3)6. Calculate f(2)f(2)f(2)

STEP 3

The **domain** is all the possible *x-values* the graph can have.Looking at our graph, it keeps going to the left and right forever!

STEP 4

So, the domain is all real numbers, which we write as (−∞,∞)(-\infty, \infty)(−∞,∞) in interval notation.

STEP 5

The **range** is all possible *y-values*.The graph goes up forever from −3-3−3, but it never goes lower than −3-3−3.

STEP 6

So, the range is from negative infinity up to and including −3-3−3.In interval notation, that's (−∞,−3](-\infty, -3](−∞,−3].Notice the square bracket because −3-3−3 is included!

STEP 7

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

STEP 8

Looking at our graph, it crosses the x-axis at x=3x = 3x=3.So, the x-intercept is **3**.

STEP 9

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

STEP 10

Our graph crosses the y-axis at y=−3y = -3y=−3.So, the y-intercept is **-3**.

STEP 11

f(−3)f(-3)f(−3) means we want to find the y-value when x=−3x = -3x=−3.

STEP 12

Looking at the graph, when x=−3x = -3x=−3, it looks like y=−6y = -6y=−6.So, f(−3)=−6f(-3) = -6f(−3)=−6.

STEP 13

f(2)f(2)f(2) means we're looking for the y-value when x=2x = 2x=2.

STEP 14

From the graph, when x=2x = 2x=2, it seems like y=−4y = -4y=−4.Therefore, f(2)=−4f(2) = -4f(2)=−4.

STEP 15

* **Domain:** (−∞,∞)(-\infty, \infty)(−∞,∞) * **Range:** (−∞,−3](-\infty, -3](−∞,−3] * **x-intercept:** 333 * **y-intercept:** −3-3−3 * f(−3)=−6f(-3) = -6f(−3)=−6 * f(2)=−4f(2) = -4f(2)=−4

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1. Find the Domain
2. Find the Range
3. Find the x-intercept(s)
4. Find the y-intercept
5. Calculate $f(-3)$
6. Calculate $f(2)$

The domain is all the possible x-values the graph can have.
Looking at our graph, it keeps going to the left and right forever!

So, the domain is all real numbers, which we write as $(-\infty, \infty)$ in interval notation.

The range is all possible y-values.
The graph goes up forever from $-3$ , but it never goes lower than $-3$ .

So, the range is from negative infinity up to and including $-3$ .
In interval notation, that's $(-\infty, -3]$ .
Notice the square bracket because $-3$ is included!

The x-intercept is where the graph crosses the x-axis.
That happens when $y = 0$ .

Looking at our graph, it crosses the x-axis at $x = 3$ .
So, the x-intercept is 3.

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

Our graph crosses the y-axis at $y = -3$ .
So, the y-intercept is -3.

$f(-3)$ means we want to find the y-value when $x = -3$ .

Looking at the graph, when $x = -3$ , it looks like $y = -6$ .
So, $f(-3) = -6$ .

$f(2)$ means we're looking for the y-value when $x = 2$ .

From the graph, when $x = 2$ , it seems like $y = -4$ .
Therefore, $f(2) = -4$ .

* Domain: $(-\infty, \infty)$ * Range: $(-\infty, -3]$ * x-intercept: $3$ * y-intercept: $-3$ * $f(-3) = -6$ * $f(2) = -4$