Question

Jasmine evaluated a function.

Function: f(x) = 3 + √x-11
Step 1: f(60) = 3 + √60-11
Step 2: f(60) = 3 + √71
Step 3: f(60) = 3 + 8.42
Step 4: f(60) = 11.41

First, identify the step which was done wrong. Then, correctly evaluate the function.

Answer 1

Can you help identify if I did the functions right?
1: f(4) = 2x + 7
response: f(4) = 15

2: f(-4) = 1/2x - 3
response: f(-4) = -5

3: f(-4) = |x| + 5
response: f(-4) = 9

Answer 2

Oh, no. I seemed to have misunderstood the first question. I read -4 as 4 instead.

Answer 3

Let's evaluate the function \( f(x) = 3 + \sqrt{x - 11} \) and identify the error in Jasmine's calculation.

Step 1: Evaluate \( f(60) \):
\[
f(60) = 3 + \sqrt{60 - 11}
\]
\[
f(60) = 3 + \sqrt{49}
\]
\[
f(60) = 3 + 7
\]
\[
f(60) = 10
\]

Now, let's identify the mistake in Jasmine's original evaluation steps.

- In Step 1, Jasmine correctly set up \( f(60) = 3 + \sqrt{60 - 11} \).
- In Step 2, Jasmine incorrectly computed \( \sqrt{60 - 11} \) as \( \sqrt{71} \) instead of \( \sqrt{49} \).
- The calculations following that were based on this incorrect value.

Thus, the error is in Step 2 where the square root calculation was incorrect.

The correct evaluation of \( f(60) \) is:
\[
f(60) = 10
\]

Answer 4

Let's evaluate each function step by step to check the calculations.

### 1. For the function \( f(x) = 2x + 7 \):
Evaluate \( f(4) \):
\[
f(4) = 2(4) + 7
\]
\[
f(4) = 8 + 7
\]
\[
f(4) = 15
\]
**Your response is correct**: \( f(4) = 15 \).

---

### 2. For the function \( f(x) = \frac{1}{2}x - 3 \):
Evaluate \( f(-4) \):
\[
f(-4) = \frac{1}{2}(-4) - 3
\]
\[
f(-4) = -2 - 3
\]
\[
f(-4) = -5
\]
**Your response is correct**: \( f(-4) = -5 \).

---

### 3. For the function \( f(x) = |x| + 5 \):
Evaluate \( f(-4) \):
\[
f(-4) = |-4| + 5
\]
\[
f(-4) = 4 + 5
\]
\[
f(-4) = 9
\]
**Your response is correct**: \( f(-4) = 9 \).

---

In summary, all of your calculations and responses for each of the functions are correct!

Answer 5

No problem! Let’s re-evaluate the first function, this time for \( f(-4) \) instead of \( f(4) \):

### 1. For the function \( f(x) = 2x + 7 \):
Evaluate \( f(-4) \):
\[
f(-4) = 2(-4) + 7
\]
\[
f(-4) = -8 + 7
\]
\[
f(-4) = -1
\]

So the correct evaluation for \( f(-4) = 2(-4) + 7 \) is **\(-1\)**, not \( 15 \).

### Summary of Results:
1. For \( f(-4) = 2x + 7 \), the correct value is **\(-1\)**.
2. For \( f(-4) = \frac{1}{2}x - 3 \), your response was correct: **\(-5\)**.
3. For \( f(-4) = |x| + 5 \), your response was correct: **\(9\)**.

Let me know if you need further assistance!