Question

1. Explain the similarities and differences between the graphs of y = 5x and y = 3x. Include domain, range, intervals of increase/decrease intercepts, and
asymptotes
2. Explain the similarities and differences between the graphs of y = 4 and y = (2) Include domain, range, intervals of increaseldecrease intercepts, and
asymptotes

Answer 1

Answer:

1. Equal domain, range, interval of increase and lack of asymptotes

The difference is the difference in slope

2. Equal domain, range, no increase or decrease (constant value) and lack of asymptotes

The difference is the difference in the y-intercept

Step-by-step explanation:

1. The similarities between the functions, y = 5·x and y = 3·x are;

a. The domain of y = 5·x is the set of all real numbers and the range is (-∞; ∞)

b.There are no critical point and the interval of increase is (-∞; ∞)

There are no asymptotes the line crosses the origin

The x and y intercept are both zero

Similarly, The domain of y = 3·x is the set of all real numbers and the range is (-∞; ∞)

There are no critical point and the interval of increase is (-∞; ∞)

There are no asymptotes the line crosses the origin

The x and y intercept are both zero

The difference between the functions, y = 5·x and y = 3·x is that the slope of y = 5·x is 5 and the slope of y = 3·x is 3

2.

The similarities between the functions, y = 4 and y = (2)  are;

a. The domain of y = 4 is the set of all real numbers (-∞; ∞), $\left \{ x\mid x\in R \right \}$ and the range is {4}

b.There are no critical point and no interval of increase or decrease

There are no asymptotes the line does not cross the origin

There are no x-intercept and y intercept is (0, 4)

Similarly, the domain of y = (2) is the set of all real numbers (-∞; ∞), $\left \{ x\mid x\in R \right \}$ and the range is {2}

There are no critical point and no interval of increase or decrease

There are no asymptotes the line does not cross the origin

There are no x-intercept and y intercept is (0, 2)

The difference between the functions, y = 4 and y = (2) is that the y-intercept of y = 4 is 4 and  the y-intercept of y = (2) is 2