Functions and Their Characteristics

What is the translated function of f(x)=2√x+1 -3 if it is translated 4 units down and 5 units to the right?

What is the domain of the function g(x)=½√x-1 +4?

What is the range of the function g(x)=½√x-1 +4?

Will a graph with a circle represent a function?

What is the domain of the function f(x)-g(x) given f(x)=3x+2 and g(x)=x²-2?

What is the domain of the function f(x) × g(x) given f(x)=3x+2 and g(x)=x²-2?

What is the domain of the function -5/k(x) given k(x)=1/x?

What is the domain of the function (g o f)(x) given f(x)=3x+2 and g(x)=x²-2?

What is the domain of the function h(x)/g(x) given h(x)=√x+3 and g(x)=x²-2?

What is the domain of the expression k(5)-g(3) given k(x)=1/x and g(x)=x²-2?

What is the domain of the expression f(g(-3)) given f(x)=3x+2 and g(x)=x²-2?

Are the functions f(x)=1/5 x +4/5 and g(x)=5x-4 inverse functions?

What is the inverse of the function g(x)=x-5/2x+3?

Rewrite the equation w = 2.16h³ as solved for 'h'.

If the weight is 22,700 g, what is the height in cm?

Find the intersection(s) of the functions f(x) = 2√x+4 -2 and g(x) = 2³√x+2 over the domain values from x = -10 to x = 10.

Translations and Functions

Translated function of f(x)=2√x+1 -3 after moving 4 units down and 5 units right is 2√(x-5) - 4.
Domain of the translated function is x ≥ 4; the range is y ≥ -7.

Domain and Range of Functions

For g(x)=½√x-1 +4:
- Domain: y ≥ 1
- Range: x ≥ 4
The inverse g⁻¹(x) has the same domain (x ≥ 4) and range (y ≥ 1) as g(x).

Function Representation

A graph with a circle does not represent a function, as it fails the vertical line test.

Function Operations

For f(x)=3x+2 and g(x)=x²-2:
- f(x) - g(x) and f(x) × g(x) require additional calculations to determine the domain; see paper for details.
Expressions involving k(x)=1/x must derive from its function rules and require calculations to establish domains.

Composition of Functions

Composition (g o f)(x) requires calculations to determine the domain; see paper for necessary computations.
Investigate if f(x)=1/5x +4/5 and g(x)=5x-4 are inverse functions through composition analysis; reasoning is needed.

Inverse of Rational Functions

The inverse of the function g(x)=(x-5)/(2x+3) is f⁻¹(x)=(-3x-5)/(2x-1).

Real-world Applications

The weight of a salt block is estimated by w = 2.16h³:
- For h: rewrites to h = ³√(w/2.16).
- If w = 22,700 g, the height h calculates to approximately 13.11 cm.

Function Intersections

To find intersections between f(x)=2√x+4 -2 and g(x)=2³√x+2 over the domain x = -10 to x = 10, calculations must be conducted by solving f(x)=g(x); see paper for more.

This quiz covers various aspects of functions, including translations, domains, ranges, and operations. Learn how to determine whether a relation represents a function and explore function compositions and inverses. Enhance your understanding of mathematical functions through practical examples.