College Algebra: Lesson 4.3a Other Common Functions
1. Linear functions: 2. Quadratic Functions3. Cubic Functions
y = x
Domain: Domain: Domain:
Range: Range: Range:
4. Absolute value functions: 5. Square root Functions6. Cube root Functions
Domain: Domain: Domain:
Range: Range: Range:
7. Reciprocal functions: 8. Exponential Functions9. Logarithmic Functions
Domain: Domain: Domain:
Range: Range: Range:
10. Least Integer Functions: 11. Greatest Integer Functions
Domain: Domain:
Range: Range:
Recall: When you graph -f(x), you reflect the graph over the x-axis.
Examples:
Consider the following function
Step 1: Indicate the general shape of the graph of the given function. click on any of the graphs to make your selection, and then submit your answer.
Step 2: Plot two points of the graph of the function, other than the origin (0,0).
A: ( , )B: ( , )
1. : 2.
3. 4.
5. Consider the following function:
Part 1: Indicate the general shape of the graph of the given function. click on any of the graphs to make your selection, and then submit your answer.
Part 2: Graph this function by indicating the length of the individual line segments, as well as the positive vertical separation between each segment of the graph.
Length:
Vertical separation:
**A piecewise defined function is a function that is defined in two (or more) pieces, each defined for a certain part of the domain. So to evaluate the function, you must look to see which "piece" of the function you use. The graph will have two different "pieces" as well.
Examples:
1. Consider the following piecewise defined function.
Step 1: Evaluate the function at x = 0. If the value is undefined, choose "undefined".
f(0)=
Step 2: Evaluate the function at x = 10. If the value is undefined, choose "undefined".
f(10)=
Step 3: Evaluate the function at x = -2. If the value is undefined, choose "undefined".
f(-2)=
2. Consider the following piecewise defined function.
Step 1: Evaluate the function at x = 2. If the value is undefined, choose "undefined".
f(2)=
Step 2: Evaluate the function at x = 4. If the value is undefined, choose "undefined".
f(4)=
Step 3: Evaluate the function at x = -1. If the value is undefined, choose "undefined".
f(-1)=
3. Consider the following function.
Step 1: Indicate the general shape of the portion of the graph of this function on the interval .
Step 2: Indicate the general shape of the portion of the graph of this function on the interval .
Step 3: Indicate which of the following four graphs is the correct graph of this piecewise defined function.
4. Consider the following function.
Step 1: Indicate the general shape of the portion of the graph of this function on the interval .
Step 2: Indicate the general shape of the portion of the graph of this function on the interval .
Step 3: Indicate which of the following four graphs is the correct graph of this piecewise defined function.