What is the domain and range of the original graph? How will the new graph look?
Domain: No. The number of months would not change. Range: Yes. The range has a new minimum value.
Practice makes perfect
The domain is all possible inputs of a relation. In this function, t represents the number of months since joining the gym. Thus, the possible values of t are greater than or equal to 0. The range is all possible outputs of a relation. In this function, C(t) represents the cost of being a gym member. We have shown the range with the red line in the graph below.
We can tell that the minimum value of the range is the y-intercept. Now, let's suppose that the gym increases its one-time joining fee and decreases its monthly membership fee. This means that the y-intercept of the graph increases and the slope decreases. What is the impact on the domain and range of the function?
Domain
The domain will stay the same. It will still start at t=0 and continue for any number of months. The line will just be less steep.
Range
We can tell that if we increase the y-intercept, the minimum value of the range will also increase. Thus, this change in the graph will have an impact on the range of the function.
