Exponential Functions and Their Graphs

The video tutorial explores exponential functions and their transformations. It begins with an introduction to the base function y = 2^x and examines how changes in the function's components affect its graph. The tutorial covers transformations such as negative exponents, which create a mirror image about the y-axis, and subtracting from the exponent, which shifts the graph horizontally. It also discusses the impact of a negative sign in front of the function, resulting in a mirror image about the x-axis, and vertical shifts caused by adding or subtracting constants. These transformations help in understanding the behavior of exponential functions.

What is the base function discussed in the video?

• y = 3^x

• y = 2^x

• y = 2x

• y = x^2

How many times is the graph of the base function drawn to illustrate its appearance?

• Five times

• Three times

• Two times

• Four times

What happens to the function when the exponent is negative?

• It becomes a mirror image about the x-axis

• It shifts downwards

• It becomes a mirror image about the y-axis

• It shifts upwards

What is the equivalent expression for y = 2^-x?

• y = 2^x

• y = 1/2^x

• y = x^2

• y = 2x

What is the effect of a negative exponent on the graph of an exponential function?

• It reflects the graph over the x-axis

• It shifts the graph downwards

• It reflects the graph over the y-axis

• It shifts the graph upwards

What is the effect of subtracting 1 from the exponent?

• The function shifts to the left

• The function shifts to the right

• The function shifts upwards

• The function shifts downwards

When x equals 2 in the function y = 2^(x-1), what is the value of y?

• 4

• 3

• 2

• 1

How does subtracting a value from the exponent affect the graph of an exponential function?

• It shifts the graph downwards

• It shifts the graph to the right

• It shifts the graph upwards

• It shifts the graph to the left

What is the effect of adding a constant to the exponent of an exponential function?

• The graph shifts downwards

• The graph shifts upwards

• The graph shifts to the right

• The graph shifts to the left

How does the graph of y = 2^x change when the exponent is decreased by 1?

• It shifts upwards

• It shifts downwards

• It shifts to the right

• It shifts to the left