Parent Functions and Transformation Review

What is the name of this function?

• Absolute Value

• Square Root

• Reciprocal

• Cubic

Answer explanation

The function named 'Absolute Value' returns the non-negative value of a number, regardless of its sign. It is distinct from the other options, which represent different mathematical operations.

Tags

CCSS.HSF.IF.A.1

CCSS.HSA.REI.D.10

CCSS.HSA.CED.A.2

What is the name of this function?

• Cube Root

• Cubic

• Quadratic

• Quartic

Answer explanation

The function described is called 'Cubic' because it involves variables raised to the third power (x^3). 'Cube Root' refers to the inverse operation, while 'Quadratic' and 'Quartic' refer to second and fourth powers, respectively.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

What is the name of this function?

• Parabola

• Quadratic

• Square Root

• Exponential Growth

Answer explanation

The function described as 'Exponential Growth' represents a rapid increase, typically modeled by the equation y = a * e^(bt). This is distinct from the other options, which represent different types of mathematical functions.

Tags

CCSS.HSF.LE.A.1

What is the name of this function?

• Quadratic

• Square Root

• Cubic

• Cube Root

Answer explanation

The function is called Quadratic because it is defined by a polynomial of degree two, typically in the form ax² + bx + c. The other options refer to different types of functions, but Quadratic is the correct choice here.

Tags

CCSS.HSA.REI.D.10

What is the name of this function?

• Square Root

• Cube Root

• Identity

• Constant

Answer explanation

The function that returns the principal square root of a number is called the Square Root. It is denoted as √x, where x is the number. The other options refer to different mathematical functions.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.A.1

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.A.2

• Left 3, Up 4, Flips, Stretch x2

• Right 3, Up 4, Flips, Stretch x2

• Right 3, Down 4, Shrink x2

• Left 3, Down 4, Shrink x2

Answer explanation

The function f(x) = -2√(x-3) + 4 shifts right by 3 (due to x-3), up by 4 (due to +4), flips vertically (due to the negative sign), and stretches vertically by a factor of 2 (due to -2). Thus, the correct choice is: Right 3, Up 4, Flips, Stretch x2.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

What is the name of this function?

• Square Root

• Radical

• Reciprocal

• Greatest Integer

Answer explanation

The correct answer is 'Reciprocal', which refers to the function that takes a number and returns its multiplicative inverse (1/x). The other options represent different mathematical functions.

What is the Parent Function for a Linear Equation?

• f(x)= x

• f(x)=|x|

• f(x)=x²

• f(x)=1/x

Answer explanation

The parent function for a linear equation is f(x) = x, which represents a straight line with a slope of 1. The other options represent different types of functions: absolute value, quadratic, and rational functions.

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

What is the Parent Function for a Absolute Value Function?

• f(x)= x

• f(x)=|x|

• x=|y|

• f(x)=|x-2|

Answer explanation

The parent function for an absolute value function is f(x)=|x|. This function outputs the non-negative value of x, making it the fundamental form of all absolute value functions.

Tags

CCSS.HSF.IF.C.7

Describe the transformations that were applied to the parent function: f(x)=|x|-5

• Shift Left 5

• Shift Up 5

• Shift Right 5

• Shift Down 5

Answer explanation

The function f(x)=|x|-5 represents a vertical shift of the parent function f(x)=|x|. The '-5' indicates that the graph is shifted down by 5 units, making 'Shift Down 5' the correct transformation.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5