Question

the figure above is the graph of the function m(t). let n(t) = m(t) + 2, k(t) = m(t + 1.5), w(t) = m(t - 0.5) - 2.5 and p(t) = m(t - 1). find the values of the following: 1. n(-3)= 2. n(2)= 3. k(2.5)= 4. w(1.5)= 5. w(-1.5)= 6. p(2)=

Explanation:

Step1: Identify $m(-3)$ from graph

From the graph, $m(-3) = -1$

Step2: Calculate $n(-3)$

$n(t)=m(t)+2$, so $n(-3)=m(-3)+2 = -1 + 2 = 1$

Step3: Identify $m(2)$ from graph

From the graph, $m(2) = 6$

Step4: Calculate $n(2)$

$n(2)=m(2)+2 = 6 + 2 = 8$

Step5: Rewrite $k(2.5)$ using definition

$k(t)=m(t+1.5)$, so $k(2.5)=m(2.5+1.5)=m(4)$

Step6: Identify $m(4)$ from graph

From the graph, $m(4) = 6$

Step7: Rewrite $w(1.5)$ using definition

$w(t)=m(t-0.5)-2.5$, so $w(1.5)=m(1.5-0.5)-2.5=m(1)-2.5$

Step8: Identify $m(1)$ from graph

From the graph, $m(1) = 8$

Step9: Calculate $w(1.5)$

$w(1.5)=8 - 2.5 = 5.5$

Step10: Rewrite $w(-1.5)$ using definition

$w(-1.5)=m(-1.5-0.5)-2.5=m(-2)-2.5$

Step11: Identify $m(-2)$ from graph

From the graph, $m(-2) = 2$

Step12: Calculate $w(-1.5)$

$w(-1.5)=2 - 2.5 = -0.5$

Step13: Rewrite $p(2)$ using definition

$p(t)=m(t-1)$, so $p(2)=m(2-1)=m(1)$

Step14: Identify $m(1)$ from graph

From the graph, $m(1) = 8$

Answer:

1. $n(-3)=1$
2. $n(2)=8$
3. $k(2.5)=6$
4. $w(1.5)=5.5$
5. $w(-1.5)=-0.5$
6. $p(2)=8$