If the temperature goes up 1 degree Celsius, then it goes up 1.8 degrees Fahrenheit. [tex]0^{\circ}[/tex] Celsius equals [tex]32^{\circ}[/tex] Fahrenheit.

1. Write a function [tex]f(c)[/tex] to convert Celsius to Fahrenheit.
[tex]f(c) = \square[/tex]

2. Is it possible for a temperature to be the same in degrees Celsius and Fahrenheit?
Possible same temperature is [tex]\square[/tex].

To convert a temperature from Celsius to Fahrenheit, you can use the function [tex]\( f(c) \)[/tex] which is based on the relationship between Celsius and Fahrenheit. The formula is:

[tex]\[ f(c) = c \times 1.8 + 32 \][/tex]

This formula takes a temperature in degrees Celsius, multiplies it by 1.8 (since an increase of 1 degree Celsius corresponds to an increase of 1.8 degrees Fahrenheit), and then adds 32 to adjust for the difference in the starting points of the two scales (0°C equals 32°F).

Now, to check if there's a temperature where the value is the same in both Celsius and Fahrenheit, we set up an equation:

Let [tex]\( c \)[/tex] be the temperature in degrees Celsius and degrees Fahrenheit. We want to solve for [tex]\( c \)[/tex] in the equation:

[tex]\[ c = c \times 1.8 + 32 \][/tex]

Rearrange this equation to isolate [tex]\( c \)[/tex]:

1. Subtract [tex]\( c \times 1.8 \)[/tex] from both sides:
[tex]\[ c - c \times 1.8 = 32 \][/tex]

2. Factor out [tex]\( c \)[/tex]:
[tex]\[ c \times (1 - 1.8) = 32 \][/tex]

3. Simplify the expression in parentheses:
[tex]\[ c \times (-0.8) = 32 \][/tex]

4. Solve for [tex]\( c \)[/tex]:
[tex]\[ c = \frac{32}{-0.8} \][/tex]

Dividing 32 by -0.8 gives:

[tex]\[ c = -40 \][/tex]

Thus, the temperature where Celsius and Fahrenheit are the same is [tex]\(-40\)[/tex] degrees.