Graphing Functions and Writing Equations

This video tutorial covers function notation, explaining how to write equations using it and the roles of dependent and independent variables. It distinguishes between linear and non-linear functions, using graphs to illustrate the differences. Real-life examples, such as babysitting and tutoring, demonstrate the application of function notation. The tutorial also guides viewers in identifying variables and writing equations, graphing them, and solving for unknowns. A comparison of savings plans is used to apply these concepts practically. The video concludes with a summary and homework instructions.

What is the function notation for y if y is dependent on x?

• x = f(y)

• f = y(x)

• x = y(f)

• y = f(x)

Which of the following is a linear function?

• y = x^2 + 3

• y = 2^x

• y = 3/x

• y = 2x + 3

How do you identify the y-intercept on a graph?

• Look for the highest point on the graph

• Look for where the graph crosses the y-axis

• Look for the lowest point on the graph

• Look for where the graph crosses the x-axis

In the example of Tasha babysitting, what is the independent variable?

• The total number of clients

• The amount of money she earns

• The number of hours she works

• The rate she charges per hour

What does evaluating a function mean?

• Calculating the output for a given input

• Finding the minimum value of the function

• Finding the maximum value of the function

• Determining the slope of the function

If a math tutor charges $35 per hour, what is the function notation for the total cost?

• f(x) = 35x

• f(x) = x/35

• f(x) = x + 35

• f(x) = 35 - x

How do you solve for x in the equation f(x) = -3x + 1 when f(x) = -20?

• x = -6

• x = 6

• x = -7

• x = 7

What is the y-intercept in the equation y = 1/2x - 2?

• 1/2

• -2

• 0

• 2

In the savings plan comparison, what is the initial amount saved by the friend?

• $150

• $200

• $250

• $300

Which variable is usually represented by x in function notation?

• Independent variable

• Total cost

• Total earnings

• Dependent variable