Question

11)

x	h(x)
5	9
6	7
-5	-2
9	1

$h(6) = \underline{\quad\quad}$
$h(-5) = \underline{\quad\quad}$
solve: $h(x) = 9$
$x = \underline{\quad\quad}$

12)
$x$: 1, 2, 3, 4
$f(x)$: 3, 7, 8, 8
(connected by mapping arrows)
$f(2) = \underline{\quad\quad}$
$f(1) = \underline{\quad\quad}$
solve: $f(x) = 7$
$x = \underline{\quad\quad}$

1. the graph of $k(x)$ is shown below.

$k(2) = \underline{\quad\quad}$
$k(-2) = \underline{\quad\quad}$
$k(0) = \underline{\quad\quad}$
$k(5) = \underline{\quad\quad}$
solve: $k(x) = 1 \
ightarrow x = \underline{\quad\quad}$ and $x = \underline{\quad\quad}$

1. the graph of $g(x)$ is shown below.

$g(-4) = \underline{\quad\quad}$
$g(4) = \underline{\quad\quad}$
$g(0) = \underline{\quad\quad}$
$g(-2) = \underline{\quad\quad}$
solve: $g(x) = 5 \
ightarrow x = \underline{\quad\quad}$

1. the graphs of $f(x)$ and $g(x)$ are shown below.

$f(5) = \underline{\quad\quad}$
$g(6) = \underline{\quad\quad}$
true or false? $f(8) > g(8)$ $\underline{\quad\quad}$
true or false? $f(2) = g(4)$ $\underline{\quad\quad}$
true or false? $f(6) < g(2)$ $\underline{\quad\quad}$

• solve: $f(x) = 6 \

ightarrow x = \underline{\quad\quad}$ and $x = \underline{\quad\quad}$

• solve: $g(x) = 0 \

ightarrow x = \underline{\quad\quad}$

• solve: $f(x) = g(x) \

ightarrow x = \underline{\quad\quad}$ and $x = \underline{\quad\quad}$

Explanation:

Step1: Evaluate h(6) from table

Find x=6, h(x)=7.

Step2: Evaluate h(-5) from table

Find x=-5, h(x)=-2.

Step3: Solve h(x)=9

Find h(x)=9, x=5.

Step4: Evaluate f(2) from mapping

Find x=2, f(x)=7.

Step5: Evaluate f(1) from mapping

Find x=1, f(x)=3.

Step6: Solve f(x)=7

Find f(x)=7, x=2.

Step7: Evaluate k(2) from graph

Find x=2, k(x)=4.

Step8: Evaluate k(-2) from graph

Find x=-2, k(x)=2.

Step9: Evaluate k(0) from graph

Find x=0, k(x)=-3.

Step10: Evaluate k(5) from graph

Find x=5, k(x)=3.

Step11: Solve k(x)=1

Find y=1, x=-5 and x=3.

Step12: Evaluate g(-4) from graph

Find x=-4, g(x)=5.

Step13: Evaluate g(4) from graph

Find x=4, g(x)=5.

Step14: Evaluate g(0) from graph

Find x=0, g(x)=1.

Step15: Evaluate g(-2) from graph

Find x=-2, g(x)=2.

Step16: Solve g(x)=5

Find y=5, x=-4 and x=4.

Step17: Evaluate f(5) from graph

Find x=5, f(x)=6.

Step18: Evaluate g(6) from graph

Find x=6, g(x)=0.

Step19: Check f(8)>g(8)

f(8)=10, g(8)=0, 10>0: True.

Step20: Check f(2)=g(4)

f(2)=2, g(4)=5, 2≠5: False.

Step21: Check f(6)<g(2)

f(6)=6, g(2)=6, 6≮6: False.

Step22: Solve f(x)=6

Find y=6, x=1 and x=5.

Step23: Solve g(x)=0

Find y=0, x=0 and x=6.

Step24: Solve f(x)=g(x)

Find intersections, x=2 and x=6.

Answer:

1. $h(6)=7$; $h(-5)=-2$; $x=5$
2. $f(2)=7$; $f(1)=3$; $x=2$
3. $k(2)=4$; $k(-2)=2$; $k(0)=-3$; $k(5)=3$; $x=-5$ and $x=3$
4. $g(-4)=5$; $g(4)=5$; $g(0)=1$; $g(-2)=2$; $x=-4$ and $x=4$
5. $f(5)=6$; $g(6)=0$; $f(8)>g(8)$: True; $f(2)=g(4)$: False; $f(6)