Math Practice Questions PDF

## Math Problems and Solutions ### 10. Inverse of a Function * Find the inverse of $f(x) = -4x + 2$ $f^{-1}(x) = -\frac{x}{4} + \frac{1}{2}$ ### 11. Perpendicular Line * Select the line that is perpendicular to the following equation: $y = \frac{1}{5}x$ * [A] $y = -5x + 1$ * [...

## Math Problems and Solutions ### 10. Inverse of a Function * Find the inverse of $f(x) = -4x + 2$ $f^{-1}(x) = -\frac{x}{4} + \frac{1}{2}$ ### 11. Perpendicular Line * Select the line that is perpendicular to the following equation: $y = \frac{1}{5}x$ * [A] $y = -5x + 1$ * [B] $y = -\frac{1}{5}x + 1$ * [C] $y = 5x + 1$ ### 12. Parallel Line * Select the line that is parallel to the following equation: $y = \frac{2}{5}x$ * [A] $y = -\frac{2}{5}x + 2$ * [B] $y = -2x + 2$ * [C] $y = \frac{2}{5}x + 2$ ### 13. Parallel and Perpendicular Equations Write an equation in slope-intercept form that is parallel to, and a second equation that is perpendicular to $y = \frac{1}{3}x + 2$ and passes through the point $(3, -2)$. #### Parallel Equation: $y = \frac{1}{3}x - 3$ 1. Keep the same slope. 2. Substitute $(3, -2)$ into the formula $y - (-2) = (\frac{1}{3})x - 1$. 3. Simplify: $y + 2 = (\frac{1}{3})x - 1$ 4. Isolate y: $y = (\frac{1}{3})x - 3$ #### Perpendicular Equation: $y = -3x + 7$ 1. The negative reciprocal of $\frac{1}{3}$ is $-3$ (slope). 2. Substitute $(3, -2)$ into $y - (-2) = -3(x - 3)$. 3. Then $y + 2 = -3x + 9$. 4. Isolate y: $y = -3x + 7$ --- ### 1. Point-Slope Form * Write an equation that represents a line passing through the point (8, 33) with a slope of 3 in point-slope form. * $m = 3, (8, 33)$ $(y - y_1) = m(x - x_1)$ $(y - 33) = 3(x - 8)$ ### 2. Slope and Y-Intercept * Determine the slope, $m$, and y-intercept, $b$, of a line that passes through the points $(2, 4)$ and $(-4, 1)$. $y=mx+b$ $4 = \frac{1}{2}(2) + b$ $y = \frac{1}{2}x + 3$ $m= \frac{1}{2}$ $4 = 1 + b$ $b = 3$ ### Popcorn Problem A movie theater sells popcorn in a reusable bucket for \$3.50. They offer refills for \$2.50 each. Write an equation in slope-intercept form to model the cost in dollars, $y$, for $x$ refills. $y = 2.5x + 3.5$ y-intercept = 3.50 m=2.50 $y - (-2) = 4(x - 5)$ $y+2 = 4x -20$ $y = 4x - 22$ * Write an equation in any form that represents a line passing through the point (5, -2) with a slope of 4. $(y - y_1) = m(x - x_1)$ $-2 = 4(5) + b$ $y = 4x - 22$ $-2 = 20 + b$ $-20 \ \ -20$ $-22=b$ * Write the equation of the line represented by $(y - 12) = -2(x + 4)$ in slope-intercept form. *Slop is -2 and passes through (-12,4)* $y = -2x - 20$ $m = -2$ $(-12, 4)$ $4=-2(-12) +b$ $4=24+b$ $-24 \ \ -24$ $-20 = b$ --- ### 6. Point-Slope Equation * Determine the values of m, x₁ and $y_1$ for the point-slope equation: $y + 3 = 4(x + 7)$ $m = 4, x1 = -7, y1 = -3$ $(y-y_1) = m(x - x_1)$ $(x - (-7))$ ### 7. Modeling a Line * Write an equation that models the line on the graph in any form. The line passes through points (-1,-2) and (3,2) $(y-y_1) = m(x - x_1)$ $m = 2$ $(y - 2) = 2(x - 3)$ ### 8. Function Operations * These ordered pairs define a function. * $\{(1, 1), (\frac{1}{2}, 2), (7, 3)\}$ * Select all ordered pairs that are in the inverse of the function. * (1, 1) * (2, $\frac{1}{2}$) * (3, 7) * List the three ordered pairs that represent the inverse of the relation shown on the graph. *The graph has the following three dots, they are:* * (-3, -2) * (-2, 0) * (-1, 2)