Exponential Functions and Transformations

The video tutorial explains how to graph exponential functions using transformations. It covers the function form y = a * B^(x-H) + K, detailing the roles of each parameter. Three examples are provided to illustrate graphing techniques, including vertical stretches, shrinks, reflections, and shifts. The video emphasizes understanding the base, asymptotes, and the effects of transformations on the graph's shape and position.

What is the general form of an exponential function?

• y = a * x^(b-h) + k

• y = a * b^(x-h) + k

• y = a * x^b + h

• y = a * b^x + h

What does the base 'b' indicate when it is greater than 1?

• Constant function

• Exponential growth

• Exponential decay

• Linear growth

If the base 'b' is between 0 and 1, what type of function is it?

• Exponential decay

• Linear function

• Quadratic function

• Exponential growth

What happens when the absolute value of 'a' is greater than 1?

• Horizontal shrink

• Vertical shrink

• Vertical stretch

• Horizontal stretch

What effect does a negative 'a' have on the graph?

• Reflects over the x-axis

• Reflects over the origin

• Reflects over the y-axis

• No reflection

What type of transformation is applied when 'a' is negative?

• Vertical stretch

• Vertical shrink

• Reflection over x-axis

• Reflection over y-axis

What is the effect of a vertical stretch on the graph?

• Stretches the graph vertically

• Compresses the graph horizontally

• Shifts the graph up

• Shifts the graph down

How does a vertical shrink affect the graph?

• Stretches the graph horizontally

• Shifts the graph right

• Compresses the graph vertically

• Shifts the graph left

What is the effect of a vertical stretch by a factor of 2?

• Divides y-values by 2

• Subtracts 2 from y-values

• Adds 2 to y-values

• Multiplies y-values by 2

What is the effect of a vertical shrink by a factor of 1/2?

• Multiplies y-values by 2

• Divides y-values by 2

• Adds 1/2 to y-values

• Multiplies y-values by 1/2