Understanding Transformations and Functions

This video tutorial covers transformations of functions, including vertical and horizontal shifts, reflections, and inverse functions. It explains parent functions, their graphs, domain, range, and end behavior. The video also delves into exponential and logarithmic functions, discussing their properties and asymptotes. Trigonometric functions, including sine, cosine, and tangent, are explored, along with their inverse functions. The tutorial provides a comprehensive overview of these mathematical concepts, aiding in understanding their graphical representations and behaviors.

What transformation occurs when a function is multiplied by a factor greater than 1?

• Vertical stretch

• Horizontal stretch

• Vertical shrink

• Horizontal shrink

What is the domain of the parent function y = x^2?

• x ≠ 0

• x ≤ 0

• x ≥ 0

• All real numbers

How does the graph of y = |x| change when it is transformed to y = |x| - 2?

• Shifts right 2 units

• Shifts left 2 units

• Shifts down 2 units

• Shifts up 2 units

What is the range of the cube root function y = ∛x?

• y ≠ 0

• All real numbers

• y ≤ 0

• y ≥ 0

Which of the following describes the end behavior of the function y = 1/x?

• As x approaches zero, y approaches zero

• As x approaches infinity, y approaches infinity

• As x approaches zero, y approaches infinity

• As x approaches infinity, y approaches zero

What is the vertical asymptote of the function y = 1/(x-2)?

• y = 2

• x = 0

• y = 0

• x = 2

What is the domain of the exponential function y = e^x?

• x ≠ 0

• All real numbers

• x < 0

• x > 0

How does the graph of y = log(x) change when it is transformed to y = log(x - 3)?

• Shifts up 3 units

• Shifts down 3 units

• Shifts left 3 units

• Shifts right 3 units

What is the period of the sine function y = sin(x)?

• 4π

• π/2

• 2π

• π

What is the range of the cosine function y = cos(x)?

• 0 to 1

• -1 to 1

• -∞ to ∞

• All real numbers