Graphing Exponential Functions in Mathematics

The video tutorial explains how to sketch the graph of the exponential function y = -2 * 3^x + 5. It begins by analyzing the behavior of the function as x becomes very negative or positive, identifying a horizontal asymptote at y = 5. The tutorial then demonstrates how to graph the function by selecting specific x-values and calculating corresponding y-values. Finally, it verifies the graph's accuracy and concludes the lesson.

What type of function is y = -2 * 3^x + 5?

• Linear

• Quadratic

• Exponential

• Logarithmic

As x becomes very negative, what does 3^x approach?

• Negative infinity

• Five

• Zero

• Infinity

What is the horizontal asymptote of the function y = -2 * 3^x + 5?

• y = 0

• y = -2

• y = 3

• y = 5

What is the value of y when x is 0 in the function y = -2 * 3^x + 5?

• 3

• 1

• 7

• 5

What is the value of y when x is 1 in the function y = -2 * 3^x + 5?

• 1

• 0

• -1

• 2

As x becomes very positive, what happens to the term -2 * 3^x?

• It approaches zero

• It becomes very positive

• It becomes very negative

• It remains constant

What is the y-intercept of the function y = -2 * 3^x + 5?

• (0, 1)

• (0, 3)

• (0, 5)

• (0, -2)

What is the behavior of the function as x approaches negative infinity?

• y approaches 0

• y approaches -2

• y approaches infinity

• y approaches 5

What is the behavior of the function as x approaches positive infinity?

• y approaches 0

• y approaches -2

• y approaches negative infinity

• y approaches 5

What is the purpose of moving the points and the asymptote in the graph?

• To ensure the graph accurately represents the exponential function

• To change the function

• To adjust the y-intercept

• To make the graph look like a line