Effects of Exponential Functions

This tutorial covers exponential functions, focusing on the standard form y = a * b^x. It explains how the 'a' value affects the graph, causing vertical stretching or shrinking. The video demonstrates graphing functions with different 'a' values, including negative ones, which reflect the graph. It concludes with translating exponential functions, discussing horizontal and vertical shifts.

What is the standard form of an exponential function?

• y = a + b^x

• y = a * b^x

• y = a / b^x

• y = a - b^x

What happens to the graph of y = b^x when 'a' is a fraction between 0 and 1?

• The graph stretches vertically

• The graph shrinks vertically

• The graph shifts horizontally

• The graph remains unchanged

If 'a' is greater than 1, what is the effect on the graph of y = b^x?

• The graph shifts horizontally

• The graph remains unchanged

• The graph shrinks vertically

• The graph stretches vertically

In the function y = 1/4 * 2^x, what is the value of y when x = 0?

• 1/4

• 1/2

• 1

• 2

For the function y = 4 * 2^x, what is the value of y when x = 2?

• 32

• 8

• 4

• 16

What is the effect on the graph of y = 2 * 2^x when 'a' is negative?

• The graph shifts horizontally

• The graph reflects across the x-axis

• The graph stretches vertically

• The graph remains unchanged

In the function y = -2 * 2^x, what is the value of y when x = 1?

• -4

• -2

• -8

• -16

What type of translation occurs when a constant is added inside the exponent of an exponential function?

• No translation

• Horizontal translation

• Reflection

• Vertical translation

In the function y = 2^(x + 3), what is the effect on the graph?

• Shifted 3 units up

• Shifted 3 units down

• Shifted 3 units right

• Shifted 3 units left

What is the effect of a positive constant outside the exponent in an exponential function?

• Positive vertical translation

• Negative vertical translation

• Positive horizontal translation

• Negative horizontal translation