What Is The Value Of $f(4)$, If $f(x) = -4(x + 3) - 14$?i) 42 Ii) -24 Iii) -42 Iv) 8

What is the Value of $f(4)$ in the Function $f(x) = -4(x + 3) - 14$?

Understanding the Function

The given function is $f(x) = -4(x + 3) - 14$. To find the value of $f(4)$, we need to substitute $x = 4$ into the function and simplify the expression.

Step 1: Substitute $x = 4$ into the Function

We will replace every instance of $x$ with $4$ in the function $f(x) = -4(x + 3) - 14$.

$$f(4) = -4(4 + 3) - 14$$

Step 2: Simplify the Expression

Now, we will simplify the expression inside the parentheses first.

$$f(4) = -4(7) - 14$$

Step 3: Multiply and Simplify

Next, we will multiply $-4$ by $7$ and then subtract $14$ from the result.

$$f(4) = -28 - 14$$

Step 4: Final Calculation

Finally, we will add $-28$ and $-14$ to get the final value of $f(4)$.

$$f(4) = -42$$

Conclusion

Therefore, the value of $f(4)$ in the function $f(x) = -4(x + 3) - 14$ is $-42$.

Answer Options

i) 42 ii) -24 iii) -42 iv) 8

Correct Answer

The correct answer is iii) -42.

Explanation

The correct answer is iii) -42 because we substituted $x = 4$ into the function and simplified the expression to get $f(4) = -42$.

Tips and Tricks

• When substituting values into a function, make sure to replace every instance of the variable with the given value.
• Simplify expressions inside parentheses first.
• Multiply and simplify the expression next.
• Finally, perform the final calculation to get the value of the function.

Practice Problems

Try substituting different values into the function $f(x) = -4(x + 3) - 14$ to practice finding the value of the function.
Q&A: Understanding the Function $f(x) = -4(x + 3) - 14$

Q: What is the value of $f(0)$ in the function $f(x) = -4(x + 3) - 14$?

A: To find the value of $f(0)$, we need to substitute $x = 0$ into the function and simplify the expression.

$$f(0) = -4(0 + 3) - 14$$

$$f(0) = -4(3) - 14$$

$$f(0) = -12 - 14$$

$$f(0) = -26$$

Q: What is the value of $f(-2)$ in the function $f(x) = -4(x + 3) - 14$?

A: To find the value of $f(-2)$, we need to substitute $x = -2$ into the function and simplify the expression.

$$f(-2) = -4(-2 + 3) - 14$$

$$f(-2) = -4(1) - 14$$

$$f(-2) = -4 - 14$$

$$f(-2) = -18$$

Q: What is the value of $f(5)$ in the function $f(x) = -4(x + 3) - 14$?

A: To find the value of $f(5)$, we need to substitute $x = 5$ into the function and simplify the expression.

$$f(5) = -4(5 + 3) - 14$$

$$f(5) = -4(8) - 14$$

$$f(5) = -32 - 14$$

$$f(5) = -46$$

Q: What is the value of $f(-1)$ in the function $f(x) = -4(x + 3) - 14$?

A: To find the value of $f(-1)$, we need to substitute $x = -1$ into the function and simplify the expression.

$$f(-1) = -4(-1 + 3) - 14$$

$$f(-1) = -4(2) - 14$$

$$f(-1) = -8 - 14$$

$$f(-1) = -22$$

Q: What is the value of $f(1)$ in the function $f(x) = -4(x + 3) - 14$?

A: To find the value of $f(1)$, we need to substitute $x = 1$ into the function and simplify the expression.

$$f(1) = -4(1 + 3) - 14$$

$$f(1) = -4(4) - 14$$

$$f(1) = -16 - 14$$

$$f(1) = -30$$

Q: What is the value of $f(-3)$ in the function $f(x) = -4(x + 3) - 14$?

A: To find the value of $f(-3)$, we need to substitute $x = -3$ into the function and simplify the expression.

$$f(-3) = -4(-3 + 3) - 14$$

$$f(-3) = -4(0) - 14$$

$$f(-3) = -14$$

Q: What is the value of $f(2)$ in the function $f(x) = -4(x + 3) - 14$?

A: To find the value of $f(2)$, we need to substitute $x = 2$ into the function and simplify the expression.

$$f(2) = -4(2 + 3) - 14$$

$$f(2) = -4(5) - 14$$

$$f(2) = -20 - 14$$

$$f(2) = -34$$

Conclusion

In this Q&A article, we have found the values of the function $f(x) = -4(x + 3) - 14$ for different values of $x$. We have seen that the function can be used to find the value of the function for any given value of $x$.