Question

unit 3: relations and functions
homework 4: function notation
& evaluating functions
this is a 2 - page document!
if $f(x) = -3x - 2$, find each value.

1. $f(3)$
2. $f(-7)$
3. $f(-2) + 9$

if $h(x) = x^2 - 5x + 7$, find each value.

1. $h(2)$
2. $h(-5)$
3. $\frac{1}{3} cdot h(-8)$

Explanation:

Step1: Substitute $x=3$ into $f(x)$

$f(3) = -3(3) - 2$

Step2: Calculate the result

$f(3) = -9 - 2 = -11$

Step1: Substitute $x=-7$ into $f(x)$

$f(-7) = -3(-7) - 2$

Step2: Calculate the result

$f(-7) = 21 - 2 = 19$

Step1: Substitute $x=-2$ into $f(x)$

$f(-2) = -3(-2) - 2$

Step2: Calculate $f(-2)$ then add 9

$f(-2) = 6 - 2 = 4$
$f(-2) + 9 = 4 + 9 = 13$

Step1: Substitute $x=2$ into $h(x)$

$h(2) = (2)^2 - 5(2) + 7$

Step2: Calculate the result

$h(2) = 4 - 10 + 7 = 1$

Step1: Substitute $x=-5$ into $h(x)$

$h(-5) = (-5)^2 - 5(-5) + 7$

Step2: Calculate the result

$h(-5) = 25 + 25 + 7 = 57$

Step1: Substitute $x=-8$ into $h(x)$

$h(-8) = (-8)^2 - 5(-8) + 7$

Step2: Calculate $h(-8)$ then multiply by $\frac{1}{3}$

$h(-8) = 64 + 40 + 7 = 111$
$\frac{1}{3} \cdot h(-8) = \frac{1}{3} \times 111 = 37$

Answer:

1. $-11$
2. $19$
3. $13$
4. $1$
5. $57$
6. $37$