Question Yes No

Studdy Solution

STEP 1

1. The function $f(x) = \frac{x^2 - 7}{x - 3}$ is defined except where the denominator is zero.
2. To determine if the point $(-2, \frac{3}{5})$ is on the graph of $f$ , we need to evaluate $f(-2)$ and check if it equals $\frac{3}{5}$ .

STEP 2

1. Substitute $x = -2$ into the function $f(x)$ .
2. Simplify the expression to find $f(-2)$ .
3. Compare the result with $\frac{3}{5}$ .
4. Determine if the point $(-2, \frac{3}{5})$ is on the graph based on the comparison.

STEP 3

Substitute $x = -2$ into the function $f(x) = \frac{x^2 - 7}{x - 3}$ .
$f(-2) = \frac{(-2)^2 - 7}{-2 - 3}$

STEP 4

Simplify the expression in the numerator and the denominator.
$(-2)^2 = 4$ $4 - 7 = -3$ $-2 - 3 = -5$ Thus, $f(-2) = \frac{-3}{-5}$

STEP 5

Simplify the fraction.
$f(-2) = \frac{-3}{-5} = \frac{3}{5}$

STEP 6

Compare $f(-2)$ with $\frac{3}{5}$ .
Since $f(-2) = \frac{3}{5}$ , the point $(-2, \frac{3}{5})$ is on the graph.
Solution: Yes

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