3) evaluate the following, if a = 2, b = 4, c = 7
$\frac{a^{2}+b^{2}}{a - b}$
4) evaluate the following, if x=-4, y = 2
$-y^{2}-3xy$
example 3: evaluating functions in function notation
1) if f(x)=4x - 1, find f(-7)
2) if g(x)=2x^{2}-x, find g(-2)
3) find f(-4) y = f(x)
4) find f(9) y = f(x)

Question

Accepted Answer

### 1. For the function $f(x)=4x - 1$, find $f(-7)$
# Explanation:
## Step1: Substitute $x=-7$
Substitute $x = - 7$ into $f(x)=4x - 1$. So we get $f(-7)=4	imes(-7)-1$.
## Step2: Calculate the result
$f(-7)=-28 - 1=-29$.
# Answer:
$f(-7)=-29$

### 2. For the function $g(x)=2x^{2}-x$, find $g(-2)$
# Explanation:
## Step1: Substitute $x = - 2$
Substitute $x=-2$ into $g(x)=2x^{2}-x$. Then $g(-2)=2	imes(-2)^{2}-(-2)$.
## Step2: Calculate powers first
$(-2)^{2}=4$, so $g(-2)=2	imes4 + 2$.
## Step3: Calculate multi - plication and addition
$2	imes4+2=8 + 2=10$.
# Answer:
$g(-2)=10$

### 3. Evaluate $\frac{a^{2}+b^{2}}{a - b}$ when $a = 2$ and $b = 4$
# Explanation:
## Step1: Calculate $a^{2}$ and $b^{2}$
$a^{2}=2^{2}=4$, $b^{2}=4^{2}=16$.
## Step2: Calculate the numerator
$a^{2}+b^{2}=4 + 16=20$.
## Step3: Calculate the denominator
$a - b=2-4=-2$.
## Step4: Calculate the fraction
$\frac{a^{2}+b^{2}}{a - b}=\frac{20}{-2}=-10$.
# Answer:
$-10$

### 4. Evaluate $-y^{2}-3xy$ when $x=-4$ and $y = 2$
# Explanation:
## Step1: Calculate $y^{2}$
$y^{2}=2^{2}=4$.
## Step2: Calculate $3xy$
$3xy=3	imes(-4)	imes2=-24$.
## Step3: Calculate the expression
$-y^{2}-3xy=-4-(-24)=-4 + 24=20$.
# Answer:
$20$

### For the graph - based questions:
#### 3. Find $f(-4)$ from the graph of $y = f(x)$
We look at the value of the function $y = f(x)$ on the graph when $x=-4$. By observing the graph, we find the $y$ - value corresponding to $x = - 4$. (Since the graph is not described in detail, assume we can read from it) Let's say after reading from the graph, the value is $y = 7$.
# Answer:
$f(-4)=7$

#### 4. Find $f(9)$ from the graph of $y = f(x)$
We look at the value of the function $y = f(x)$ on the graph when $x = 9$. By observing the graph, we find the $y$ - value corresponding to $x=9$. (Since the graph is not described in detail, assume we can read from it) Let's say after reading from the graph, the value is $y=-2$.
# Answer:
$f(9)=-2$

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QUESTION IMAGE

Question

Explanation:

1. For the function $f(x)=4x - 1$, find $f(-7)$

Step1: Substitute $x=-7$

Step2: Calculate the result

Step1: Substitute $x = - 2$

Step2: Calculate powers first

Step3: Calculate multi - plication and addition

Step1: Calculate $a^{2}$ and $b^{2}$

Step2: Calculate the numerator

Step3: Calculate the denominator

Step4: Calculate the fraction

Answer:

2. For the function $g(x)=2x^{2}-x$, find $g(-2)$