unit 5 lesson 2 practice problem 1 c and d\nthe thermostat in an empty apartment is set to 65°f from 4:00…

unit 5 lesson 2 practice problem 1 c and d\nthe thermostat in an empty apartment is set to 65°f from 4:00 a.m. to 5:00 p.m. and to 50°f from 5:00 p.m. until 4:00 a.m. here is a graph of the function h that gives the temperature h(x) in degrees fahrenheit in the apartment x hours after midnight.\n1. the owner of the apartment decides to change to a new schedule and they set the thermostat to change 3 hours later in the morning and the evening. on the same axes, sketch a graph of the new function, g, giving the temperature as a function of time.\nsketch the graph in your workbook to assist in answering the following questions.\nc.) if h(6.5)=65, then what is the corresponding point on the graph of g? use function notation to describe the point on the graph of g.\ng\n\n=\n\nd.) write an expression for g in terms of h.\ng(x)=\n

unit 5 lesson 2 practice problem 1 c and d\nthe thermostat in an empty apartment is set to 65°f from 4:00 a.m. to 5:00 p.m. and to 50°f from 5:00 p.m. until 4:00 a.m. here is a graph of the function h that gives the temperature h(x) in degrees fahrenheit in the apartment x hours after midnight.\n1. the owner of the apartment decides to change to a new schedule and they set the thermostat to change 3 hours later in the morning and the evening. on the same axes, sketch a graph of the new function, g, giving the temperature as a function of time.\nsketch the graph in your workbook to assist in answering the following questions.\nc.) if h(6.5)=65, then what is the corresponding point on the graph of g? use function notation to describe the point on the graph of g.\ng\n\n=\n\nd.) write an expression for g in terms of h.\ng(x)=\n

Answer

Explanation:

Step1: Analyze the time - shift

The new function $G$ is a time - shifted version of $H$. The thermostat schedule is changed 3 hours later in the morning and evening. This means the graph of $G$ is the graph of $H$ shifted 3 units to the right.

Step2: Find the corresponding point for part c

If $H(6.5)=65$, for the function $G$ which is $H$ shifted 3 units to the right, the input value for $G$ will be $x = 6.5+3=9.5$. So the corresponding point on the graph of $G$ is $G(9.5)=65$.

Step3: Find the expression for part d

Since $G$ is a right - shift of $H$ by 3 units, the general rule for a right - shift of a function $y = H(x)$ by $a$ units is $y=H(x - a)$. Here $a = 3$, so $G(x)=H(x - 3)$.

Answer:

c. $G(9.5)=65$ d. $G(x)=H(x - 3)$