Day 49 roots (algebra 2)

Front

What is the domain of the function defined as f(x) = -3√(x-2) + 1?

Back

Domain: [2, ∞) - The function is defined for x values greater than or equal to 2.

Front

What is the range of the function defined as f(x) = -3√(x-2) + 1?

Back

Range: (-∞, 1] - The maximum value of the function is 1 when x = 2.

Front

How do you find the x-intercept of a function?

Back

Set f(x) = 0 and solve for x. For example, for f(x) = -3√(x-2) + 1, set -3√(x-2) + 1 = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What is the x-intercept of the function f(x) = -3√(x-2) + 1?

Back

(2, 0) - The x-intercept occurs when the function equals zero.

Tags

CCSS.HSF-IF.C.7B

Front

What does it mean for a function to be reflected over the x-axis?

Back

The output values (y-values) of the function are multiplied by -1, flipping the graph vertically.

Tags

CCSS.HSF.BF.B.3

Front

What is a vertical stretch in the context of function transformations?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

Describe the transformation: f(x) = -3√(x-2) + 1 compared to the parent function f(x) = √x.

Back

Reflected over the x-axis, vertical stretch by 3, shifted right 2, and shifted up 1.

Tags

CCSS.HSF.BF.B.3

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

What is the y-intercept of the function f(x) = -3√(x-2) + 1?

Back

(0, 3) - The y-intercept occurs when x = 0.

Tags

CCSS.HSF-IF.C.7B

Front

How do you determine the range of a function?

Back

Analyze the output values (y-values) of the function based on its domain and behavior.