Advanced Algebra and Functions Flashcards

What is the value of g(12) for the function g defined by g(x) = 3(x + 8)?

What is an equation of the line that passes through the point (0, 0) and is perpendicular to the line shown?

What is the surface area of a right rectangular prism with length 4 cm, width 9 cm, and height 3 cm?

Which expression is equivalent to (x + 7)(x² - 3x + 2)?

What does the equation C = 7/5 p indicate about the cost of pears?

Which of the following is the graph of a function where Y = f(x)?

Which expression is equivalent to 3x² + 6x - 24?

What equation gives the expected number of bacteria after x days for an initial population of 500? The population doubles every 4 hours.

Which value of x satisfies the equation x² + 5x - 9 = 5?

Which equation could define f(x) for the graph of y = f(x)?

How would you best describe the range of y = -2x⁴ + 7?

If cos A = 5/8 in right triangle ABC, what is the value of cos B?

Functions and Equations

Function ( g ) is defined by ( g(x) = 3(x + 8) ), producing ( g(12) = 60 ).
Equation of a line through point (0,0) and perpendicular to a given line is ( y = \frac{5}{4}x ).

Geometry and Surface Area

The surface area of a right rectangular prism (length = 4 cm, width = 9 cm, height = 3 cm) is calculated as ( 2(lw + lh + wh) ), yielding an area of ( 150 , \text{cm}^2 ).

Algebraic Expressions

The expression ( (x + 7)(x^2 - 3x + 2) ) simplifies to ( x^3 + 4x^2 - 19x + 14 ).
The expression ( 3x^2 + 6x - 24 ) can be factored as ( 3(x - 2)(x + 4) ).

Cost Comparisons

For pears with cost ( C = \frac{7}{5}p ), apples cost approximately $0.07 less per pound than pears.

Graphing Functions

The graph that represents a function ( Y = f(x) ) is labeled as option C.

Exponential Growth

A population of 500 bacteria doubles every 4 hours, described by the equation ( n = 500(2)^{6x} ) for ( x ) in days.

Solving Equations

The solution to the equation ( x^2 + 5x - 9 = 5 ) is ( x = -7 ).

Quadratic Functions

The quadratic function ( f(x) = x^2 - 2x - 8 ) could represent the given graph of ( y = f(x) ).

Trigonometry in Right Triangles

In triangle ABC with angle C as a right angle, if ( \cos A = \frac{5}{8} ), then ( \cos B = \frac{39}{8} ).

Function Range Analysis

The range of the function ( y = -2x^4 + 7 ) indicates ( y \leq 7 ), suggesting a maximum point.

Test your knowledge of advanced algebra concepts and functions with these flashcards. Each question challenges your understanding of equations, functions, and geometric calculations. Perfect for students looking to reinforce their algebra skills!