Question

optional - ungraded ch 3 practice quizoptional - ungraded ch 3 practice quizscore: 13/40 answered: 4/7question 6characteristics of linear functionscomplete the table below.| function | rate of change | initial value | behavior || ---- | ---- | ---- | ---- || $f(x)=2x - 9$ | | | select an answer || $v(t)=6 - 6t$ | | | select an answer || $r(a)=4a$ | | | select an answer || $c(w)=-7$ | | | select an answer |

Explanation:

Step1: Identify rate of change (slope)

For a linear function in form $f(x)=mx+b$, $m$ is the rate of change.

• $f(x)=2x-9$: Rate of change = $2$
• $V(t)=6-6t$: Rate of change = $-6$
• $r(a)=4a$: Rate of change = $4$
• $C(w)=-7$: Rate of change = $0$

Step2: Identify initial value (y-intercept)

The initial value is $b$ in $f(x)=mx+b$ (value when input is 0).

• $f(x)=2x-9$: Initial value = $-9$
• $V(t)=6-6t$: Initial value = $6$
• $r(a)=4a$: Initial value = $0$
• $C(w)=-7$: Initial value = $-7$

Step3: Determine behavior

• Positive rate of change: Increasing
• Negative rate of change: Decreasing
• Zero rate of change: Constant
• $f(x)=2x-9$: Increasing
• $V(t)=6-6t$: Decreasing
• $r(a)=4a$: Increasing
• $C(w)=-7$: Constant

Answer:

Function	Rate of Change	Initial Value	Behavior
$V(t)=6-6t$	$-6$	$6$	Decreasing
$r(a)=4a$	$4$	$0$	Increasing
$C(w)=-7$	$0$	$-7$	Constant