Exponential and Logarithmic Functions

The video tutorial covers graphing techniques for exponential and logarithmic functions. It begins with an introduction to graphing and a recap of previous lessons on polynomial and absolute value functions. The instructor explains the relevance of exponential and logarithmic functions in real-world scenarios, such as population growth and carbon dating. The tutorial then provides a detailed guide on graphing exponential functions, highlighting key features like shape, intercept, asymptote, and point for scale. Finally, it covers graphing logarithmic functions, emphasizing their inverse relationship with exponential graphs.

What topic is the class continuing with this week?

• Trigonometry

• Statistics

• Graphing

• Polynomial functions

Why are exponential and logarithmic functions relevant to current situations?

• They are irrelevant to real-world applications.

• They are used in cooking recipes.

• They help in understanding population growth and virus spread.

• They are only used in ancient mathematics.

What characterizes an exponential graph?

• It decreases as it gets larger.

• It grows faster as it gets larger.

• It remains constant regardless of size.

• It grows slower as it gets larger.

What is an example of exponential decay?

• Carbon-14 dating

• Economic inflation

• Human population growth

• Virus spread

What are the four key features to look for when graphing exponential and logarithmic functions?

• Color, size, shape, and texture

• Shape, intercept, asymptote, and point for scale

• Length, width, height, and depth

• Origin, axis, slope, and intercept

What is the first feature to consider when graphing an exponential function?

• Point for scale

• Intercept

• Asymptote

• Shape

What is the intercept of the exponential graph y = 2^x?

• x-intercept at 0

• y-intercept at 1

• x-intercept at 1

• y-intercept at 0

What is the asymptote of the exponential graph y = 2^x?

• Horizontal asymptote at y = 0

• Horizontal asymptote at x = 1

• Vertical asymptote at x = 0

• Vertical asymptote at y = 1

What is the point for scale on the exponential graph y = 2^x?

• (1, 0)

• (0, 1)

• (1, 2)

• (2, 1)

How does a logarithmic graph differ from an exponential graph?

• It decreases rapidly.

• It gets steeper and steeper.

• It remains constant.

• It gets shallower and shallower.