2.5 Question 46 (extraneous)

[Eigenvalue]

Precalculus
Michael Sullivan
Edition 4
Chapter 2, Section 2.5

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting.Start with the graph of the parent function (e.g. y=x²) and show all stages. Be sure to show at least 3 key points. Find the domain and range of the function.

f(x)=(x+2)³-3

[Eigenvalue]

parent function: f(x)=x³

1. Shift left 2 units on the x-axis f(x)=(x+2)³
2. Shift down 3 units on the y-axis f(x)=(x+2)³-3

Domain: all real numbers, as the domain for any cubic function is all real numbers

Range: all real numbers, as the range for any cubic function is all real numbers

x-intercept: Set f(x)=0
0=(x+2)³-3
(x+2)³=3
x+2=[tex]\sqrt[3]{3}[/tex]
x=[tex]\sqrt[3]{3}[/tex]-2
Coordinate for x-intercept: ([tex]\sqrt[3]{3}[/tex]-2, 0)

y-intercept: Set x=0
f(x)=(0+2)³-3
f(x)=8-3
f(x)=5
Coordinate for y-intercept: (0,5)

Turning points (when the graph changes from increasing to decreasing, or vice versa): no turning points, as the graph is increasing for all real numbers

Increasing: all real numbers