Math / Algebra

QuestionFind the indicated intercept(s) of the graph of the function. $y$ -intercept of $f(x)=\frac{x-2}{x^{2}+10 x-11}$

Studdy Solution

STEP 1

What is this asking? Find where the graph of the function crosses the $\text{y}$ -axis. Watch out! Remember that the $\text{y}$ -intercept happens when $x = 0$ !

STEP 2

1. Substitute $x = 0$
2. Simplify the expression

STEP 3

Alright, let's kick things off by finding the $\text{y}$ -intercept!
To do this, we need to figure out the value of $f(x)$ when $x$ is zero.
So, we'll substitute $x = 0$ into our function:
$f(0) = \frac{0 - 2}{0^2 + 10 \cdot 0 - 11}$

STEP 4

Remember, we're doing this because the $\text{y}$ -intercept is the point where the graph of the function intersects the $\text{y}$ -axis.
And guess what?
On the $\text{y}$ -axis, the value of $x$ is always zero!

STEP 5

Now, let's simplify that expression we just got!
In the numerator, we have $0 - 2$ , which simplifies to $-2$ .
$f(0) = \frac{-2}{0^2 + 10 \cdot 0 - 11}$

STEP 6

In the denominator, we've got $0^2 + 10 \cdot 0 - 11$ .
Well, $0^2$ is just $0$ , and $10 \cdot 0$ is also $0$ .
So, the denominator simplifies to $0 + 0 - 11$ , which is $-11$ .
$f(0) = \frac{-2}{-11}$

STEP 7

We now have a fraction with a negative number in both the numerator and the denominator.
Remember, a negative divided by a negative gives us a positive!
So, $\frac{-2}{-11}$ simplifies to $\frac{2}{11}$ .
$f(0) = \frac{2}{11}$

STEP 8

So, the $\text{y}$ -intercept is at $\left( 0, \frac{2}{11} \right)$ !

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QuestionFind the indicated intercept(s) of the graph of the function. $y$ -intercept of $f(x)=\frac{x-2}{x^{2}+10 x-11}$

Studdy Solution

STEP 1

What is this asking? Find where the graph of the function crosses the $\text{y}$ -axis. Watch out! Remember that the $\text{y}$ -intercept happens when $x = 0$ !

STEP 2

1. Substitute $x = 0$
2. Simplify the expression

STEP 3

Alright, let's kick things off by finding the $\text{y}$ -intercept!
To do this, we need to figure out the value of $f(x)$ when $x$ is zero.
So, we'll substitute $x = 0$ into our function:
$f(0) = \frac{0 - 2}{0^2 + 10 \cdot 0 - 11}$

STEP 4

Remember, we're doing this because the $\text{y}$ -intercept is the point where the graph of the function intersects the $\text{y}$ -axis.
And guess what?
On the $\text{y}$ -axis, the value of $x$ is always zero!

STEP 5

Now, let's simplify that expression we just got!
In the numerator, we have $0 - 2$ , which simplifies to $-2$ .
$f(0) = \frac{-2}{0^2 + 10 \cdot 0 - 11}$

STEP 6

In the denominator, we've got $0^2 + 10 \cdot 0 - 11$ .
Well, $0^2$ is just $0$ , and $10 \cdot 0$ is also $0$ .
So, the denominator simplifies to $0 + 0 - 11$ , which is $-11$ .
$f(0) = \frac{-2}{-11}$

STEP 7

We now have a fraction with a negative number in both the numerator and the denominator.
Remember, a negative divided by a negative gives us a positive!
So, $\frac{-2}{-11}$ simplifies to $\frac{2}{11}$ .
$f(0) = \frac{2}{11}$

STEP 8

So, the $\text{y}$ -intercept is at $\left( 0, \frac{2}{11} \right)$ !

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QuestionFind the indicated intercept(s) of the graph of the function. yyy-intercept of f(x)=x−2x2+10x−11f(x)=\frac{x-2}{x^{2}+10 x-11}f(x)=x2+10x−11x−2​

Studdy Solution

STEP 1

What is this asking? Find where the graph of the function crosses the y\text{y}y-axis. Watch out! Remember that the y\text{y}y-intercept happens when x=0x = 0x=0!

STEP 2

1. Substitute x=0x = 0x=02. Simplify the expression

STEP 3

STEP 4

Remember, we're doing this because the y\text{y}y-intercept is the point where the graph of the function *intersects* the y\text{y}y-axis.And guess what?On the y\text{y}y-axis, the value of xxx is *always* **zero**!

STEP 5

Now, let's **simplify** that expression we just got!In the numerator, we have 0−20 - 20−2, which simplifies to −2-2−2.f(0)=−202+10⋅0−11 f(0) = \frac{-2}{0^2 + 10 \cdot 0 - 11} f(0)=02+10⋅0−11−2​

STEP 6

In the denominator, we've got 02+10⋅0−110^2 + 10 \cdot 0 - 1102+10⋅0−11.Well, 020^202 is just 000, and 10⋅010 \cdot 010⋅0 is also 000.So, the denominator simplifies to 0+0−110 + 0 - 110+0−11, which is −11-11−11.f(0)=−2−11 f(0) = \frac{-2}{-11} f(0)=−11−2​

STEP 7

We now have a fraction with a negative number in both the numerator *and* the denominator.Remember, a negative divided by a negative gives us a **positive**!So, −2−11\frac{-2}{-11}−11−2​ simplifies to 211\frac{2}{11}112​.f(0)=211 f(0) = \frac{2}{11} f(0)=112​

STEP 8

So, the y\text{y}y-intercept is at (0,211)\left( 0, \frac{2}{11} \right)(0,112​)!

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QuestionFind the indicated intercept(s) of the graph of the function. $y$ -intercept of $f(x)=\frac{x-2}{x^{2}+10 x-11}$

What is this asking? Find where the graph of the function crosses the $\text{y}$ -axis. Watch out! Remember that the $\text{y}$ -intercept happens when $x = 0$ !

1. Substitute $x = 0$
2. Simplify the expression

Remember, we're doing this because the $\text{y}$ -intercept is the point where the graph of the function intersects the $\text{y}$ -axis.
And guess what?
On the $\text{y}$ -axis, the value of $x$ is always zero!

Now, let's simplify that expression we just got!
In the numerator, we have $0 - 2$ , which simplifies to $-2$ .
$f(0) = \frac{-2}{0^2 + 10 \cdot 0 - 11}$

In the denominator, we've got $0^2 + 10 \cdot 0 - 11$ .
Well, $0^2$ is just $0$ , and $10 \cdot 0$ is also $0$ .
So, the denominator simplifies to $0 + 0 - 11$ , which is $-11$ .
$f(0) = \frac{-2}{-11}$

We now have a fraction with a negative number in both the numerator and the denominator.
Remember, a negative divided by a negative gives us a positive!
So, $\frac{-2}{-11}$ simplifies to $\frac{2}{11}$ .
$f(0) = \frac{2}{11}$

So, the $\text{y}$ -intercept is at $\left( 0, \frac{2}{11} \right)$ !