Math 3 Unit 4 Families of Functions Flashcard #1 2024

Front

What is the general form of a square root function?

Back

The general form of a square root function is y = √(x - h) + k, where (h, k) is the vertex of the graph.

Tags

CCSS.HSF-IF.C.7B

Front

How does the graph of y = (x + 5)^3 - 1 differ from the parent function y = x^3?

Back

The graph of y = (x + 5)^3 - 1 is a transformation of the parent function y = x^3, shifted left 5 units and down 1 unit.

Tags

CCSS.HSF.BF.B.3

Front

What is the first step in solving the equation 2|x + 7| - 1 = 9?

Back

The first step is to isolate the absolute value by adding 1 to both sides, resulting in 2|x + 7| = 10.

Front

What does the absolute value represent in a mathematical equation?

Back

The absolute value represents the distance of a number from zero on the number line, regardless of direction.

Tags

CCSS.6.NS.C.7C

Front

What is the effect of the transformation y = (x - 2)^3 - 4 on the graph of y = x^3?

Back

The transformation shifts the graph of y = x^3 right 2 units and down 4 units.

Tags

CCSS.HSF.BF.B.3

Front

How do you find the vertex of a square root function in the form y = √(x - h) + k?

Back

The vertex of the function is the point (h, k).

Tags

CCSS.HSF-IF.C.7B

Front

What is the significance of the coefficient in front of the absolute value in an equation like 2|x + 7|?

Back

The coefficient affects the steepness of the graph; a larger coefficient makes the graph steeper.

Front

What are the key characteristics of cubic functions?

Back

Cubic functions have one or two turning points, can have both positive and negative values, and their end behavior is such that as x approaches ±∞, y approaches ±∞.

Front

How do you graph a function like y = √(x - 1) - 3?

Back

To graph y = √(x - 1) - 3, plot the vertex at (1, -3) and then plot points to the right, as the square root function only exists for x ≥ 1.

Tags

CCSS.HSA.CED.A.2

Front

What is the domain of the function y = √(x - 1)?

Back

The domain is x ≥ 1, as the expression under the square root must be non-negative.