Question

1. evaluate the expressions below using the given function equations and graph.

$b(x)=\frac{x}{2}$
$k(x)=-2x + 6$

a. $k(1)-h(10)$
$k(1)=-2(1)+6=4$
$h(10)=\frac{10}{2}=5$
$4 - 5=-1$

b. $g(-4)$
$g(-4)=2$

c. $h(0)=\frac{0}{2}$

d. $x$ when $g(x)=1$
$x=-6,-2,6$

e. $x$ when $k(x)$

c. $g(3)-k(3)$
$g(3)=5$
$k(3)=-2\times3+6=0$
$g(3)-k(3)=5 - 0=5$

1. aubrey wants to take a trip to powell books in portland. she lives in issaquah. she drives toward miles towards portland and stops at a friends house in renton first. once she leaves renton, she drive at a constant speed of 60 miles per hour.

a. write a function, $f(t)$, that models the distance the car is from issaquah over time in hours leaving renton, $t$.
$f(t)=5 + 60t$

b. how far from issaquah will aubrey have traveled in total after 2 hours?

c. if portland is 150 miles away from issaquah, how long will it take aubrey to get there? round to two decimal places.
$150=5 + 60t$
$\frac{145}{60}=\frac{60t}{60}$
$t\approx2.42$ hrs

1. use the elevator graph to the right to answer the questions.

a. what is $f(0)$, and what does it mean in the context of the problem?

b. find and interpret the average rate of change of the elevator.
$\frac{-3}{2}\to-3$ floors every 2 seconds the elevator goes down 3 floors

Explanation:

Step1: Analyze the function for part a

The function \( f(t) \) models the distance from Issaquah. She has already driven 5 miles (to Renton) and then drives at 60 miles per hour. Using the formula \( \text{distance}=\text{initial distance}+\text{speed}\times\text{time} \), we get \( f(t)=5 + 60t \).

Step2: Calculate for part b

Substitute \( t = 2 \) into \( f(t) \).

$$
LATEXBLOCK0
$$

Step3: Solve for part c

Set \( f(t)=150 \) (since Portland is 150 miles from Issaquah) and solve for \( t \).

$$
LATEXBLOCK1
$$

Answer:

a. \( f(t)=5 + 60t \)
b. 125 miles
c. Approximately \( 2.42 \) hours