Graphing Exponential Functions: Key Concepts and Techniques

The video tutorial explores graphing exponential functions, focusing on transformations such as shifts. It begins with graphing f(x) = 2^(x+4), explaining the horizontal shift. Then, it examines g(x) = 2^x + 4, highlighting the vertical shift. The tutorial concludes with a discussion on the problems with negative base exponentials, emphasizing why they are not typically used.

What does the function f(x) = 2^(x+4) represent in terms of graphical transformation?

• Horizontal shift to the left by 4 units

• Horizontal shift to the right by 4 units

• Vertical shift upwards by 4 units

• No shift, just scaling

What does the exponent in the function 2^(x+4) indicate about its graph?

• Horizontal shift to the right by 4 units

• Horizontal shift to the left by 4 units

• Vertical stretch by a factor of 4

• Vertical shift upwards by 4 units

What is the result of applying a horizontal shift to the left by 4 units to the function 2^x?

• 2^(x+4)

• 2^(x-4)

• 2^x - 4

• 2^x + 4

How can the function 2^(x+4) be decomposed using exponent laws?

• 2^x + 2^4

• 2^x * 2^4

• 2^(x*4)

• 2^(x/4)

What is the effect of multiplying the graph of 2^x by 16?

• Compresses the graph horizontally by a factor of 16

• Rotates the graph around the origin

• Shifts the graph 16 units up

• Expands the graph vertically by a factor of 16

What is the graphical difference between 2^(x+4) and 2^x + 4?

• Both shift the graph to the left by 4 units

• Both shift the graph upwards by 4 units

• The first shifts left by 4 units, the second shifts up by 4 units

• The first shifts up by 4 units, the second shifts left by 4 units

What happens to the graph of 2^x when you add 4 to the function?

• Shifts 4 units to the left

• Shifts 4 units to the right

• Shifts 4 units downwards

• Shifts 4 units upwards

How does adding 4 to the function 2^x change its graph?

• Shifts it 4 units downwards

• Shifts it 4 units upwards

• Shifts it 4 units to the left

• Shifts it 4 units to the right

Why are functions with negative bases like -3^x not considered valid for real number outputs?

• They result in constant values

• They result in undefined values for fractional exponents

• They only produce negative outputs

• They do not affect the graph's shape

Why is the function -3^(1/2) considered undefined?

• Negative bases are not allowed

• Square root of a negative number is not a real number

• It results in a positive number

• It does not affect the graph