How does f(t)=–2t–7 change over the interval from t= –7 to t=–6? Choices: [[f(t) decreases by 2][f(t) increases by 2][f(t) increases by 200%][f(t) decreases by a factor of 2]]

Calculate f(-7): We have the function f(t) = –2t – 7. Calculate the value of f(t) when t = –7. f(–7) = –2(–7) – 7 f(–7) = 14 – 7 f(–7) = 7Calculate f(-6): Calculate the value of f(t) when t = –6. f(–6) = –2(–6) – 7 f(–6) = 12 – 7 f(–6) = 5Find Change in f: Determine the change in f(t) over the interval from t = –7 to t = –6. Change in f(t) = f(–6) – f(–7) Change in f(t) = 5 – 7 Change in f(t) = –2Analyze Change: Analyze the change in f(t) to determine if it increases or decreases and by what factor or amount. Since the change in f(t) is –2, this means f(t) decreases by 2 as t increases from –7 to –6.

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How does $f(t)=-2t-7$ change over the interval from $t=-7$ to $t=-6$ ? $\newline$ Choices: $\newline$ $\left[\text{f(t) decreases by } 2\right]$ $\newline$ $\left[\text{f(t) increases by } 2\right]$ $\newline$ $\left[\text{f(t) increases by } 200\%\right]$ $\newline$ $\left[\text{f(t) decreases by a factor of } 2\right]$

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Math Problems

Algebra 1

Linear functions over unit intervals

Full solution

Q. How does

f(t)=-2t-7

change over the interval from

t=-7

t=-6

\newline

Choices:

\newline

\left[\text{f(t) decreases by } 2\right]

\newline

\left[\text{f(t) increases by } 2\right]

\newline

\left[\text{f(t) increases by } 200\%\right]

\newline

\left[\text{f(t) decreases by a factor of } 2\right]

Calculate $f(-7)$ : We have the function $f(t) = -2t - 7$ . Calculate the value of $f(t)$ when $t = -7$ .
$f(-7) = -2(-7) - 7$
$f(-7) = 14 - 7$
$f(-7) = 7$
Calculate $f(-6)$ : Calculate the value of $f(t)$ when $t = -6$ .
$f(-6) = -2(-6) - 7$
$f(-6) = 12 - 7$
$f(-6) = 5$
Find Change in f: Determine the change in $f(t)$ over the interval from $t = -7$ to $t = -6$ .
Change in $f(t)$ = $f(-6) - f(-7)$
Change in $f(t)$ = $5 - 7$
Change in $f(t)$ = $-2$
Analyze Change: Analyze the change in $f(t)$ to determine if it increases or decreases and by what factor or amount. $\newline$ Since the change in $f(t)$ is $–2$ , this means $f(t)$ decreases by $2$ as $t$ increases from $–7$ to $–6$ .