Question

How do the graphs of the function differ from the graph of f(x)=1.5x^3

Answer 1

Answer: p(x) = steeper

               q(x) = less steep and reflection

               r(x) = reflection

Step-by-step explanation:

The parent graph is: f(x) = 1.5x³

1. If the absolute value of the coefficient in front of x³ is greater than 1.5, then it is steeper (the graph is stretched).
2. If the absolute value of the coefficient in front of x³ is less than 1.5, then it is less steep (the graph is shrunk/compressed).
3. A negative sign in front of the coefficient represents a reflection over the x-axis.

p(x):  2 > 1.5 , so it is stretched (steeper).

p(x): coefficient has a positive sign, so it is NOT a reflection

q(x):  1  < 1.5 , so it is shrunk/compressed (less steep).

q(x): coefficient has a negative sign, so it is a reflection over x-axis

r(x): 1.5 = 1.5 so it is neither a stretch or a shrink

r(x): coefficient has a negative sign, so it is a reflection over x-axis