Math / Algebra

QuestionThe graph of a function $f$ is shown below. Find one value of $x$ for which $f(x)=4$ and find $f(0)$ . (a) One value of $x$ for which $f(x)=4$ : 0 (b) $f(0)=$ $\square$

Studdy Solution

STEP 1

What is this asking? This problem is asking us to find an $x$ value where the graph hits a height of 4, and also what height the graph has when $x$ is 0. Watch out! Don't mix up $x$ and $f(x)$ ! $f(x)$ is the height of the graph, and $x$ is how far left or right we are.

STEP 2

1. Find $x$ where $f(x) = 4$
2. Find $f(0)$

STEP 3

Alright, so we need to find an $x$ value where $f(x)$ is 4.
Remember, $f(x)$ is just another way of saying the height or the y-value of our function.
So, where does our graph have a height of 4?

STEP 4

Let's look at the graph!
We want to find a spot where the line is at a height of 4 on the vertical axis.
Imagine drawing a horizontal line across the graph at $f(x) = 4$ .

STEP 5

Boom! It looks like the line hits a height of 4 somewhere between $x = -1$ and $x = 0$ .
We just need one value of $x$ , so let's estimate.
It looks pretty close to $x = \mathbf{-1}$ , so let's go with that!

STEP 6

Now, we need to find $f(0)$ .
This means we need to find the height of the graph when $x$ is 0.

STEP 7

$x = 0$ is right in the middle, vertically.
It's where the vertical axis crosses the horizontal axis.

STEP 8

Let's look at the graph again!
When $x = 0$ , the graph seems to be right at $f(x) = \mathbf{0}$ .
So, $f(0) = \mathbf{0}$ !

STEP 9

$f(x) = 4$ when $x$ is approximately $\mathbf{-1}$ .
And $f(0) = \mathbf{0}$ .

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QuestionThe graph of a function $f$ is shown below. Find one value of $x$ for which $f(x)=4$ and find $f(0)$ . (a) One value of $x$ for which $f(x)=4$ : 0 (b) $f(0)=$ $\square$

Studdy Solution

STEP 1

What is this asking? This problem is asking us to find an $x$ value where the graph hits a height of 4, and also what height the graph has when $x$ is 0. Watch out! Don't mix up $x$ and $f(x)$ ! $f(x)$ is the height of the graph, and $x$ is how far left or right we are.

STEP 2

1. Find $x$ where $f(x) = 4$
2. Find $f(0)$

STEP 3

Alright, so we need to find an $x$ value where $f(x)$ is 4.
Remember, $f(x)$ is just another way of saying the height or the y-value of our function.
So, where does our graph have a height of 4?

STEP 4

Let's look at the graph!
We want to find a spot where the line is at a height of 4 on the vertical axis.
Imagine drawing a horizontal line across the graph at $f(x) = 4$ .

STEP 5

Boom! It looks like the line hits a height of 4 somewhere between $x = -1$ and $x = 0$ .
We just need one value of $x$ , so let's estimate.
It looks pretty close to $x = \mathbf{-1}$ , so let's go with that!

STEP 6

Now, we need to find $f(0)$ .
This means we need to find the height of the graph when $x$ is 0.

STEP 7

$x = 0$ is right in the middle, vertically.
It's where the vertical axis crosses the horizontal axis.

STEP 8

Let's look at the graph again!
When $x = 0$ , the graph seems to be right at $f(x) = \mathbf{0}$ .
So, $f(0) = \mathbf{0}$ !

STEP 9

$f(x) = 4$ when $x$ is approximately $\mathbf{-1}$ .
And $f(0) = \mathbf{0}$ .

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QuestionThe graph of a function fff is shown below. Find one value of xxx for which f(x)=4f(x)=4f(x)=4 and find f(0)f(0)f(0). (a) One value of xxx for which f(x)=4f(x)=4f(x)=4 : 0 (b) f(0)=f(0)=f(0)= □\square□

Studdy Solution

STEP 1

What is this asking? This problem is asking us to find an xxx value where the graph hits a height of 4, and also what height the graph has when xxx is 0. Watch out! Don't mix up xxx and f(x)f(x)f(x)! f(x)f(x)f(x) is the *height* of the graph, and xxx is how far left or right we are.

STEP 2

1. Find xxx where f(x)=4f(x) = 4f(x)=42. Find f(0)f(0)f(0)

STEP 3

Alright, so we need to find an xxx value where f(x)f(x)f(x) is **4**.Remember, f(x)f(x)f(x) is just another way of saying the *height* or the *y-value* of our function.So, where does our graph have a height of **4**?

STEP 4

Let's look at the graph!We want to find a spot where the line is at a height of **4** on the vertical axis.Imagine drawing a horizontal line across the graph at f(x)=4f(x) = 4f(x)=4.

STEP 5

Boom! It looks like the line hits a height of **4** somewhere between x=−1x = -1x=−1 and x=0x = 0x=0.We just need *one* value of xxx, so let's estimate.It looks pretty close to x=−1x = \mathbf{-1}x=−1, so let's go with that!

STEP 6

Now, we need to find f(0)f(0)f(0).This means we need to find the height of the graph when xxx is **0**.

STEP 7

x=0x = 0x=0 is right in the middle, vertically.It's where the vertical axis crosses the horizontal axis.

STEP 8

Let's look at the graph again!When x=0x = 0x=0, the graph seems to be right at f(x)=0f(x) = \mathbf{0}f(x)=0.So, f(0)=0f(0) = \mathbf{0}f(0)=0!

STEP 9

f(x)=4f(x) = 4f(x)=4 when xxx is approximately −1\mathbf{-1}−1.And f(0)=0f(0) = \mathbf{0}f(0)=0.

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QuestionThe graph of a function $f$ is shown below. Find one value of $x$ for which $f(x)=4$ and find $f(0)$ . (a) One value of $x$ for which $f(x)=4$ : 0 (b) $f(0)=$ $\square$

What is this asking? This problem is asking us to find an $x$ value where the graph hits a height of 4, and also what height the graph has when $x$ is 0. Watch out! Don't mix up $x$ and $f(x)$ ! $f(x)$ is the height of the graph, and $x$ is how far left or right we are.

1. Find $x$ where $f(x) = 4$
2. Find $f(0)$

Alright, so we need to find an $x$ value where $f(x)$ is 4.
Remember, $f(x)$ is just another way of saying the height or the y-value of our function.
So, where does our graph have a height of 4?

Let's look at the graph!
We want to find a spot where the line is at a height of 4 on the vertical axis.
Imagine drawing a horizontal line across the graph at $f(x) = 4$ .

Boom! It looks like the line hits a height of 4 somewhere between $x = -1$ and $x = 0$ .
We just need one value of $x$ , so let's estimate.
It looks pretty close to $x = \mathbf{-1}$ , so let's go with that!

Now, we need to find $f(0)$ .
This means we need to find the height of the graph when $x$ is 0.

$x = 0$ is right in the middle, vertically.
It's where the vertical axis crosses the horizontal axis.

Let's look at the graph again!
When $x = 0$ , the graph seems to be right at $f(x) = \mathbf{0}$ .
So, $f(0) = \mathbf{0}$ !

$f(x) = 4$ when $x$ is approximately $\mathbf{-1}$ .
And $f(0) = \mathbf{0}$ .