Type The Correct Answer In Each Box. Use Numerals Instead Of Words.Complete The Table Of Inputs And Outputs For The Function: $f(x) = -5(x+7$\]$\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline -9 & $\square$ \\ \hline $\square$ & 0

Complete the table of inputs and outputs for the function: $f(x) = -5(x+7)$

To complete the table of inputs and outputs for the function $f(x) = -5(x+7)$, we need to substitute the given values of $x$ into the function and calculate the corresponding values of $f(x)$.

Substituting $x = -9$ into the function

We will substitute $x = -9$ into the function $f(x) = -5(x+7)$.

$f(-9) = -5(-9+7)$ $f(-9) = -5(-2)$ $f(-9) = 10$

So, the value of $f(-9)$ is $10$.

Substituting $f(x) = 0$ into the function

We will substitute $f(x) = 0$ into the function $f(x) = -5(x+7)$.

$0 = -5(x+7)$ $0 = -5x - 35$ $5x = -35$ $x = -7$

So, the value of $x$ when $f(x) = 0$ is $-7$.

The completed table of inputs and outputs for the function $f(x) = -5(x+7)$

Discussion

The function $f(x) = -5(x+7)$ is a linear function, which means it has a constant rate of change. The graph of this function is a straight line with a negative slope.

When we substitute $x = -9$ into the function, we get $f(-9) = 10$. This means that when the input is $-9$, the output is $10$.

When we substitute $f(x) = 0$ into the function, we get $x = -7$. This means that when the output is $0$, the input is $-7$.

The completed table of inputs and outputs for the function $f(x) = -5(x+7)$ shows the relationship between the input and output values of the function.

Key Takeaways

• The function $f(x) = -5(x+7)$ is a linear function with a negative slope.
• When we substitute $x = -9$ into the function, we get $f(-9) = 10$.
• When we substitute $f(x) = 0$ into the function, we get $x = -7$.
• The completed table of inputs and outputs for the function $f(x) = -5(x+7)$ shows the relationship between the input and output values of the function.

Practice Problems

• Find the value of $f(3)$ for the function $f(x) = -5(x+7)$.
• Find the value of $x$ when $f(x) = 15$ for the function $f(x) = -5(x+7)$.

Solutions to Practice Problems

• $f(3) = -5(3+7)$ $f(3) = -5(10)$ $f(3) = -50$

• $15 = -5(x+7)$ $15 = -5x - 35$ $5x = -20$ $x = -4$

Conclusion

In this article, we completed the table of inputs and outputs for the function $f(x) = -5(x+7)$. We also discussed the properties of the function and provided solutions to practice problems. The completed table of inputs and outputs for the function $f(x) = -5(x+7)$ shows the relationship between the input and output values of the function.