Question

directions: use the following functions to answer each question. use that answer to find the color. then color the picture. (note: it is possible for colors to repeat.)
$f(x) = -5x + 6$
$g(x) = x^2 + 4$
$h(x) = 3x$

$x$	$j(x)$
2	3
3	0
4	-3

(graph of $k(x)$: a parabola opening upwards)

1. find $g(-3)$
2. find $j(3) + f(3)$
3. find $3k(4)$

-2	-5	13	...	-7	-4	9	18	6
orange	white	pink	purple	red	dark blue	yellow	light blue	brown

1. find $h(x - 1)$
2. find $g(x + 4)$
3. find $f(-2x)$

$3(x - 3)$	$3x - 3$	$3x - 1$	$x^2 + 8x + 12$	$x^2 + 20$	$x^2 + 8x + 20$	$-7x - 12x$	$10x + 6$	$10x^2 + 6$
teal	dark green	orange	yellow	dark blue	light green	peach	light blue	red

Explanation:

Step1: Substitute $x=-3$ into $g(x)$

$g(-3) = (-3)^2 + 4$

Step2: Calculate value of $g(-3)$

$g(-3) = 9 + 4 = 13$

Step1: Get $j(3)$ from table, substitute $x=3$ into $f(x)$

$j(3)=0$, $f(3) = -5(3)+6$

Step2: Calculate $f(3)$ then sum

$f(3)=-15+6=-9$; $j(3)+f(3)=0+(-9)=-9$
(Note: -9 is not in the color key, but closest intended calculation confirms this result)

Step1: Identify $k(4)$ from the graph

From the parabola $k(x)$, when $x=4$, $k(4)=6$

Step2: Calculate $3k(4)$

$3k(4)=3\times6=18$

Step1: Substitute $x-1$ into $h(x)$

$h(x-1)=3(x-1)$

Step2: Simplify the expression

$h(x-1)=3x-3$

Step1: Substitute $x+4$ into $g(x)$

$g(x+4)=(x+4)^2 + 4$

Step2: Expand and simplify the expression

$(x^2+8x+16)+4=x^2+8x+20$

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

$f(-2x)=-5(-2x)+6$

Step2: Simplify the expression

$f(-2x)=10x+6$

Answer:

1. $g(-3)=13$ (Color: pink)
2. $j(3)+f(3)=-9$ (No matching color in provided key)
3. $3k(4)=18$ (Color: light blue)
4. $h(x-1)=3x-3$ (Color: dark green)
5. $g(x+4)=x^2+8x+20$ (Color: light green)
6. $f(-2x)=10x+6$ (Color: light blue)