To determine how the graph of the function will change if the initial temperature of the metal is now different, let's analyze the given function and the change in initial conditions step by step.
1. Initial function and starting temperature:
The initial function describing the temperature change per minute is given by:
[tex]\[
f(x) = 89x - 100
\][/tex]
Here, the initial temperature [tex]\(T_1\)[/tex] is [tex]\(-100^{\circ}\)[/tex] Celsius.
2. New initial temperature:
The new initial temperature [tex]\(T_2\)[/tex] is given as [tex]\(25^{\circ}\)[/tex] Celsius.
3. Change in initial temperatures:
To find how the graph of the function changes, evaluate the difference between the new initial temperature and the old initial temperature:
[tex]\[
\text{Temperature Difference} = T_2 - T_1
\][/tex]
Substituting the given temperatures:
[tex]\[
\text{Temperature Difference} = 25 - (-100)
\][/tex]
Simplifying this difference:
[tex]\[
\text{Temperature Difference} = 25 + 100 = 125
\][/tex]
4. Effect on the graph of the function:
The graph of the function will shift vertically by this difference. Since the temperature difference is positive (125 degrees), the shift will be vertically upwards.
So, the graph of the function will shift vertically up by [tex]\(125^{\circ}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\text{The line will shift vertically up by } 125^{\circ}.
\][/tex]
