Exponential Functions and Graph Analysis

The video tutorial explains how to match exponential equations to graphs by analyzing their properties. It covers exponential growth and decay, the effect of the constant k on graph shifts, and how to verify equations using specific points on the graphs. The tutorial emphasizes understanding the base and horizontal asymptote to determine the correct equation for each graph.

What is the general form of the exponential functions discussed in the video?

• f(x) = mx + c

• f(x) = b^x + k

• f(x) = ax^2 + bx + c

• f(x) = a sin(x) + b

Tags

CCSS.HSF-IF.C.8B

Which condition indicates exponential growth in the functions discussed?

• b > 1

• b = 1

• 0 < b < 1

• b < 0

What happens to the graph when the value of k is increased?

• The graph shifts upwards

• The graph shifts downwards

• The graph shifts to the left

• The graph shifts to the right

Tags

CCSS.HSF-IF.C.7D

What is the horizontal asymptote of the red graph?

• y = 0

• y = -1

• y = -2

• y = -3

Tags

CCSS.HSF.LE.A.2

Which equation correctly represents the red graph?

• y = 1/2^x - 2

• y = 1/2^x + 2

• y = 2^x - 2

• y = 2^x + 2

What is the x-intercept of the red graph?

• (0, -1)

• (1, -1)

• (1, 0)

• (0, 0)

Tags

CCSS.HSF-IF.C.7D

What is the horizontal asymptote of the blue graph?

• y = 0

• y = -1

• y = -3

• y = -2

Tags

CCSS.HSF.LE.A.2

Which equation correctly represents the blue graph?

• y = 2^x - 3

• y = 1/2^x + 3

• y = 2^x + 3

• y = 1/2^x - 3

What is the y-intercept of the blue graph?

• (1, -3)

• (0, -3)

• (1, -2)

• (0, -2)

What is the value of k for the blue graph?

• k = -2

• k = -1

• k = -3

• k = 0