Math / Algebra

Question1. Determine the $x$ -intercepts of each function. a) $f(x)=\frac{-3 x}{2 x+5}$

Studdy Solution

STEP 1

1. We are given the function $f(x) = \frac{-3x}{2x+5}$ .
2. The $x$ -intercepts of a function occur where $f(x) = 0$ .

STEP 2

1. Set the function equal to zero to find the $x$ -intercepts.
2. Solve the resulting equation for $x$ .

STEP 3

Set the function equal to zero:
$\frac{-3x}{2x+5} = 0$

STEP 4

To solve the equation, recognize that a fraction is zero when its numerator is zero (and the denominator is not zero):
$-3x = 0$

STEP 5

Solve for $x$ :
$x = 0$
The $x$ -intercept of the function $f(x) = \frac{-3x}{2x+5}$ is:
$\boxed{0}$

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Question1. Determine the $x$ -intercepts of each function. a) $f(x)=\frac{-3 x}{2 x+5}$

Studdy Solution

STEP 1

1. We are given the function $f(x) = \frac{-3x}{2x+5}$ .
2. The $x$ -intercepts of a function occur where $f(x) = 0$ .

STEP 2

1. Set the function equal to zero to find the $x$ -intercepts.
2. Solve the resulting equation for $x$ .

STEP 3

Set the function equal to zero:
$\frac{-3x}{2x+5} = 0$

STEP 4

To solve the equation, recognize that a fraction is zero when its numerator is zero (and the denominator is not zero):
$-3x = 0$

STEP 5

Solve for $x$ :
$x = 0$
The $x$ -intercept of the function $f(x) = \frac{-3x}{2x+5}$ is:
$\boxed{0}$

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Question1. Determine the xxx-intercepts of each function. a) f(x)=−3x2x+5f(x)=\frac{-3 x}{2 x+5}f(x)=2x+5−3x​

Studdy Solution

STEP 1

1. We are given the function f(x)=−3x2x+5 f(x) = \frac{-3x}{2x+5} f(x)=2x+5−3x​.2. The x x x-intercepts of a function occur where f(x)=0 f(x) = 0 f(x)=0.

STEP 2

1. Set the function equal to zero to find the x x x-intercepts.2. Solve the resulting equation for x x x.

STEP 3

Set the function equal to zero:−3x2x+5=0 \frac{-3x}{2x+5} = 0 2x+5−3x​=0

STEP 4

To solve the equation, recognize that a fraction is zero when its numerator is zero (and the denominator is not zero):−3x=0 -3x = 0 −3x=0

STEP 5

Solve for x x x:x=0 x = 0 x=0 The x x x-intercept of the function f(x)=−3x2x+5 f(x) = \frac{-3x}{2x+5} f(x)=2x+5−3x​ is:0 \boxed{0} 0​

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Question1. Determine the $x$ -intercepts of each function. a) $f(x)=\frac{-3 x}{2 x+5}$

1. We are given the function $f(x) = \frac{-3x}{2x+5}$ .
2. The $x$ -intercepts of a function occur where $f(x) = 0$ .

1. Set the function equal to zero to find the $x$ -intercepts.
2. Solve the resulting equation for $x$ .

Set the function equal to zero:
$\frac{-3x}{2x+5} = 0$

To solve the equation, recognize that a fraction is zero when its numerator is zero (and the denominator is not zero):
$-3x = 0$

Solve for $x$ :
$x = 0$
The $x$ -intercept of the function $f(x) = \frac{-3x}{2x+5}$ is:
$\boxed{0}$