LESSON 6 Exploring Functions Unit Review
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.