Questions: How many x-intercepts would the function shown below have? f(x)=5(3x+5)

How many x-intercepts would the function shown below have? f(x)=5(3x+5)
Transcript text: How many x-intercepts would the function shown below have? \[ f(x)=5(3 x+5) \]
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Solution

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Determine the number of x-intercepts of the function \( f(x) = 5(3x + 5) \).

Find the x-intercept condition.

An x-intercept occurs when \( f(x) = 0 \).

Set \( f(x) = 0 \) and solve for \( x \).

\[ 5(3x + 5) = 0 \]

Solve the equation for \( x \).

Divide both sides by 5:
\[ 3x + 5 = 0 \]
Subtract 5 from both sides:
\[ 3x = -5 \]
Divide both sides by 3:
\[ x = -\frac{5}{3} \]

The function \( f(x) = 5(3x + 5) \) has exactly one x-intercept at \( x = -\frac{5}{3} \).
\[ \boxed{1} \]

The function \( f(x) = 5(3x + 5) \) has \\(\boxed{1}\\) x-intercept.

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