Algebra: Equations and Functions

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Questions and Answers

Solve the following absolute value inequality: $|2x - 1| \leq 5$.

$-2 \leq x \leq 3$

Factor the polynomial: $x^3 - 8$.

$(x - 2)(x^2 + 2x + 4)$

Simplify the rational expression: $\frac{x^2 - 4}{x^2 - 4x + 4}$.

$\frac{x + 2}{x - 2}$

Rationalize the denominator: $\frac{3}{\sqrt{5} - \sqrt{2}}$.

<p>$\sqrt{5} + \sqrt{2}$</p> Signup and view all the answers

Given $f(x) = 2x + 3$ and $g(x) = x^2 - 1$, find $f(g(x))$.

<p>$2x^2 + 1$</p> Signup and view all the answers

Solve for $x$: $3^{2x - 1} = 81$.

<p>$\frac{5}{2}$</p> Signup and view all the answers

Solve the system of equations: $x + y = 7$ $x - y = 1$

<p>$x = 4, y = 3$</p> Signup and view all the answers

A line passes through the points (1, 5) and (3, 13). Find the equation of the line in slope-intercept form.

<p>$y = 4x + 1$</p> Signup and view all the answers

Find the domain of the function $f(x) = \sqrt{x - 4}$.

<p>$x \geq 4$</p> Signup and view all the answers

Solve for $x$: $\log_2(x) + \log_2(x - 2) = 3$.

<p>$x = 4$</p> Signup and view all the answers

Flashcards

Statistics

The science of collecting, analyzing, interpreting, and presenting data.

Algebra

Branch of mathematics manipulating symbols and the rules for manipulating those symbols.

Algebraic Equation

A statement showing the equality between two algebraic expressions.

Solving Equations

Isolate the variable on one side by performing same operations on both sides.

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Linear Equation

Equation where the highest power of the variable is 1. General form: ax + b = 0.

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Quadratic Equation

Equation where the highest power of the variable is 2. Standard form: ax^2 + bx + c = 0.

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Factoring

Expressing a quadratic expression as a product of two linear expressions.

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Completing the Square

Transforming a quadratic equation into the form (x - h)^2 = k.

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Quadratic Formula

x = (-b ± √(b^2 - 4ac)) / (2a), general solution for ax^2 + bx + c = 0.

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System of Equations

A set of two or more equations with the same variables.

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Study Notes

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