LESSON 6 Exploring Functions Unit Review

Answer 1

1. What is a function?

A function is a relationship or rule that assigns each input (or x-value) to exactly one output (or y-value).

2. What is the domain of a function?

The domain of a function is the set of all possible input values for which the function is defined.

3. What is the range of a function?

The range of a function is the set of all possible output values that the function can produce.

4. How can you determine if a given relationship is a function?

To determine if a given relationship is a function, you can use the vertical line test. If a vertical line passes through the graph of the relationship at more than one point, then it is not a function.

5. What is the difference between discrete and continuous functions?

A discrete function is a function with distinct, separate values for the input variable, while a continuous function is a function that can take any value within a given interval.

6. What is the difference between linear and nonlinear functions?

A linear function is a function whose graph is a straight line, while a nonlinear function is a function whose graph is not a straight line.

7. How can you identify the slope and y-intercept of a linear function from its equation?

In the equation of a linear function in slope-intercept form (y = mx + b), the slope (m) is the coefficient of the x-term, and the y-intercept (b) is the constant term.

8. How can you graph a linear function?

To graph a linear function, plot the y-intercept on the y-axis and use the slope to find additional points on the line. Connect the points to create a straight line.

9. What is a piecewise function?

A piecewise function is a function that is defined by different rules or formulas on different intervals of its domain.

10. How can you evaluate a function for a specific input value?

To evaluate a function for a specific input value, substitute the given input value into the function and simplify to find the corresponding output value.