Understanding Graphs: Trigonometric and Exponential Functions

This video tutorial introduces various types of graphs, focusing on trigonometric and exponential graphs. It explains the basic shapes and characteristics of sine, cosine, and tangent graphs, emphasizing recognition over memorization. The tutorial also covers exponential graphs, describing their general form and behavior. The use of calculators to aid in understanding these graphs is highlighted, ensuring students can recognize and plot these functions effectively.

Which of the following graphs is not mentioned in the introduction?

• Straight lines

• Quadratics

• Logarithmic

• Reciprocals

What is the maximum value of the sine graph?

• 2

• 1

• 0

• -1

How does the cosine graph differ from the sine graph?

• It has a different amplitude

• It is shifted horizontally

• It is shifted vertically

• It is a straight line

Which trigonometric graph crosses the y-axis at one?

• Tangent

• Cosine

• Sine

• Exponential

What is a key characteristic of the tangent graph?

• It is a parabola

• It is a circle

• It is a series of separate curves

• It is a straight line

What is the shape of the sine and cosine graphs?

• Linear

• Curved

• Triangular

• Rectangular

What is the general form of an exponential function?

• y = k^x

• y = ax^2 + bx + c

• y = sin(x)

• y = mx + c

At what point do exponential graphs typically cross the y-axis?

• (0, 0)

• (1, 1)

• (1, 0)

• (0, 1)

What happens to the exponential graph as x increases for y = 2^x?

• It decreases

• It approaches zero

• It heads towards infinity

• It remains constant

For y = 0.5^x, how does the graph behave?

• It forms a circle

• It remains constant

• It decreases

• It increases