Exploring Parent Function Graphs and Transformations

The video tutorial introduces various parent functions, including constant, linear, absolute value, quadratic, square root, and inverse functions. It explains their domains and ranges, and how transformations such as shifts and scaling affect these functions. The tutorial also covers the concept of asymptotes in inverse functions and provides examples of how to transform each function type.

What is the range of the constant function f(x) = k, where k is a real number?

• Zero to infinity

• The value k

• Negative infinity to positive infinity

• All real numbers

If a linear function f(x) = x is shifted up by 4 units, what is the new equation?

• y = x / 4

• y = 4x

• y = x - 4

• y = x + 4

What is the domain of the linear function f(x) = x?

• Only positive integers

• Zero to positive infinity

• Negative infinity to zero

• All real numbers

Why does the absolute value function f(x) = |x| remain above the x-axis?

• Because it has a slope of zero

• Because it is always negative

• Because it is a horizontal line

• Because it is always positive

If the absolute value function is shifted left by 5 units and down by 4 units, what is the new range?

• Negative 5 to infinity

• Negative 4 to infinity

• Negative infinity to 4

• 0 to infinity

What is the range of the quadratic function f(x) = x^2?

• Negative infinity to zero

• Zero to infinity

• Negative infinity to positive infinity

• All real numbers

If the quadratic function is shifted right by 6 units and up by 3 units, what is the new range?

• 0 to infinity

• Negative infinity to infinity

• 3 to infinity

• Negative infinity to 3

What is the domain of the square root function f(x) = √x?

• Negative infinity to positive infinity

• All real numbers

• Zero to positive infinity

• Negative infinity to zero

What is the domain of the inverse function f(x) = 1/x?

• All real numbers except zero

• Zero to positive infinity

• Only positive integers

• Negative infinity to zero

If the inverse function is shifted up by 2 units, what is the new horizontal asymptote?

• y = -2

• y = 2

• y = 1

• y = 0