Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar. complete the table of inputs and outputs for the given function. g(x) = 3 - 8x x g(x) 0 0 -5 3

Explanation:

Step1: Find x when g(x)=0

We know that \( g(x) = 3 - 8x \). Set \( g(x)=0 \), so we have the equation \( 0 = 3 - 8x \).
To solve for \( x \), we first add \( 8x \) to both sides: \( 8x=3 \). Then divide both sides by 8: \( x = \frac{3}{8}=0.375 \).

Step2: Find g(x) when x = 0

Substitute \( x = 0 \) into \( g(x)=3 - 8x \). So \( g(0)=3-8\times0 = 3 - 0=3 \).

Step3: Find x when g(x)= - 5

Set \( g(x)=-5 \), so \( -5 = 3 - 8x \).
Subtract 3 from both sides: \( -5 - 3=-8x \), which simplifies to \( -8=-8x \).
Divide both sides by - 8: \( x = 1 \).

Step4: Find g(x) when x = 3

Substitute \( x = 3 \) into \( g(x)=3 - 8x \). So \( g(3)=3-8\times3=3 - 24=-21 \).

Now let's fill the table:

• When \( g(x) = 0 \), \( x=\frac{3}{8}=0.375 \)
• When \( x = 0 \), \( g(x)=3 \)
• When \( g(x)=-5 \), \( x = 1 \)
• When \( x = 3 \), \( g(x)=-21 \)

So the completed table (from left to right, top to bottom for the blanks) should have:
First blank (x when g(x)=0): \( 0.375 \) (or \( \frac{3}{8} \))
Second blank (g(x) when x = 0): \( 3 \)
Third blank (x when g(x)= - 5): \( 1 \)
Fourth blank (g(x) when x = 3): \( -21 \)

Answer:

The values to fill in the blanks (from left to right, top to bottom for the empty boxes) are \( \frac{3}{8} \) (or \( 0.375 \)), \( 3 \), \( 1 \), \( -21 \) respectively. If we consider the order of the table:

• For the x - value when \( g(x)=0 \): \( \boldsymbol{\frac{3}{8}} \) (or \( 0.375 \))
• For the \( g(x) \) - value when \( x = 0 \): \( \boldsymbol{3} \)
• For the x - value when \( g(x)=-5 \): \( \boldsymbol{1} \)
• For the \( g(x) \) - value when \( x = 3 \): \( \boldsymbol{-21} \)