Algebra Functions and Equations Quiz

The points where the graph crosses the x-axis (x-intercepts) and the y-axis (y-intercepts).

Set y = 0 and solve for x. The solutions are the x-intercepts.

Set x = 0 and solve for y. The solution is the y-intercept.

The equation of a line written as y = mx + b, where m is the slope and b is the y-intercept.

Lines that have the same slope but different y-intercepts. They never intersect.

Lines whose slopes are negative reciprocals of each other. They intersect at a right angle.

(x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius.

Rewrite the equation in standard form by completing the square. The center and radius can then be read directly from the equation.

A function that reverses the effect of another function. If f(a) = b, then the inverse function, denoted as f⁻¹(b), will give you a.

Expressing a relationship between a base, exponent, and result in two different ways: Logarithmic form: logb(a) = c is equivalent to Exponential form: b^c = a.

The set of all possible input values (x) for which the logarithmic function is defined. The argument of the logarithm must be positive.

The logarithm of a product is equal to the sum of the logarithms of the factors: logb(xy) = logb(x) + logb(y)

Finding the value of the unknown variable (usually x) in an equation where the variable is in the exponent. Often involves using logarithms to isolate the variable.

Find the time (t) when the projectile reaches its highest point. This occurs at the vertex of the parabola represented by the height function.

Find the price (p) that generates the highest revenue. Set the revenue function equal to zero and solve for p. The solution is the price that maximizes revenue.

Find the values of x that satisfy the inequality. Factor the quadratic expression, find the critical points (where the expression equals zero), and test intervals around these points.

The exponent of each factor in the factored form of a polynomial tells you the multiplicity of its corresponding zero.

If a polynomial f(x) equals zero when x = c, then x - c is a factor of f(x).

These are possible rational zeros of a polynomial. They are found by taking the ratios of factors of the constant term to the factors of the leading coefficient.

Vertical asymptotes occur where the denominator of a rational function becomes zero, but the numerator does not. Factor the denominator and set it equal to zero.

Horizontal asymptotes occur when the degree of the numerator and denominator are the same, or when the denominator's degree is greater.

Finding the values of the variables that satisfy all equations in the system.

A method to solve systems of equations by adding or subtracting equations to eliminate one variable.

A method to solve systems of equations by solving one equation for one variable and substituting it into the other equation.

A system of equations with no solution. The graphs of the equations are parallel lines.

A system of equations with infinitely many solutions. The graphs of the equations are the same line.

Finding the values of x and y that satisfy both equations in the system.

A system of equations where the graphs of the equations intersect at a single point.

The solution to a system of equations is the point where the graphs of the equations intersect. This point represents the values of x and y that satisfy both equations.