Section 2.1: Functions

1. List examples of functions from everyday life and biology.

2. Specify what makes a function more specific than just “a rule that assigns outputs to inputs”.

3. Give the definition of a function.

4. Explain how the vertical line test can be used to verify if a curve in the coordinate plane is the graph of a function, and relate this to the definition of a function.

5. Define the domain and range of a function.

6. Given a function \(f\):

   • Express in words how \(f\) acts on an input \(x\) to generate an output \(f(x)\).
   • Evaluate the function at a specified input.
   • Find the domain and range of \(f\).

7. Use the ‘box’ notation on page 150 of the text as a way to think about a variable as a ‘blank space’ for the input to a function.

8. Demonstrate the correspondence between verbal, algebraic, visual, and numerical representations of a function by converting from one representation to another.

9. Evaluate a piecewise function by reading left-to-right: first determine the condition on the input \(x\), then determine the output under that condition.

Section 2.4: Average Rate of Change of a Function

1. Define the net change of a function from \(x = a\) to \(x = b\).
2. Define the average rate of change of a function \(f\) between \(x = a\) and \(x = b\) in terms of \(a, b, f(a)\), and \(f(b)\).
3. Define the average rate of change of a function as the ‘rise’ of the function over the ‘run’ of the function.
4. Relate the average rate of change of a function \(f\) to the slope of the line segment between \((a, f(a))\) and \((b, f(b))\).

Section 2.5: Linear Functions and Models

1. Explain the meaning of the statement: “the only things linear functions can do is go up, go down, or stay flat.”

2. Specify the standard form of a linear function.

3. Given a linear function in non-standard form, rewrite the function in standard form.

4. Given a function, determine whether the function is linear or nonlinear.

5. Graph a linear function given one of:

   • The equation for the function
   • The slope and intercept of the function
   • The slope and a point on the graph of the function
   • Two points on the graph of the function

6. Compute the slope of a linear function using the average rate of change of the function.

7. Compute the slope of a linear function as ‘rise over run.’

8. Determine the form of a linear function from a ‘word problem’ given the requisite information to determine the equation of a line.