Exam 1: Graphs, Functions, and Models

Write a slope-intercept equation for a line with the given characteristics. - $\left( - \frac { 1 } { 5 } , \frac { 3 } { 5 } \right) , \left( \frac { 1 } { 5 } , \frac { 7 } { 5 } \right)$ A) y=2 x B) y=2 x+1 C) $y = \frac { 7 } { 5 } x - 2$ D) y=4 x+10

Find the center and radius of the circle. - $( x + 4 ) ^ { 2 } + ( y + 9 ) ^ { 2 } = 4$ A) (4,9) ; 4 B) (-9,-4) ; 2 C) (-4,-9) ; 2 D) (9,4) ; 4

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through (7, 8), perpendicular to x = 1

Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle. -(10, 3), (16, 5), (20, -7)

Write an equation in slope-intercept form for the line shown. - A) y= 2x+4 B) y= 2x-4 C) $y = \frac { 1 } { 2 } x - 4$ D) $y = \frac { 1 } { 2 } x + 4$

Determine the domain and range of the relation. -{(7,1),(8,4),(-3,3),(-3,2)} A) Domain: {7,-3,8,-3} ; Range: {1,3,4,2} B) Domain: {1,3,4,2} ; Range: {7,-3,8} C) Domain: {7,-3,8} ; Range: {1,3,4,2} D) Domain: {7,-3,8,3} ; Range: {1,3,4,2}

Find the equation of the circle. Express the equation in standard form - A) $( x + 15 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 10 ^ { 2 }$ B) $( x + 15 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 10 ^ { 2 }$ C) $( x + 10 ) ^ { 2 } + ( y - 15 ) ^ { 2 } = 10 ^ { 2 }$ D) $( x + 10 ) ^ { 2 } + ( y + 15 ) ^ { 2 } = 10 ^ { 2 }$

Find the slope and the y-intercept of the line with the given equation. -5x-2y+5=0 A) $\frac { 5 } { 2 } ; \left( 0 , - \frac { 5 } { 2 } \right)$ B) $- \frac { 5 } { 2 } ; \left( 0 , - \frac { 5 } { 2 } \right)$ C) $- \frac { 5 } { 2 } ; \left( 0 , \frac { 5 } { 2 } \right)$ D) $\frac { 5 } { 2 } ; \left( 0 , \frac { 5 } { 2 } \right)$

Tell whether or not the relation is a function. -{(2,-7), (2,-5), (5,1), (9,-7), (10,8)}

Solve the equation. - $\frac { 1 } { 6 } x - 2 = \frac { 1 } { 4 } x - 3$ A) - 12 B) 3 C) 15 D) 12

Solve the problem. -The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. By using linear regression, the following function is obtained: y=67.3+1.07 x where x is number of hours studied and y is score on the test. Use this function to predict the score on the test of a student who studies 11 hours. Hours 5 10 4 6 10 9 Score 64 86 69 86 59 87

Tell whether or not the relation is a function. - $\{ ( - 4,3 ) , ( - 2 , - 6 ) , ( 2 , - 9 ) , ( 2 , - 2 ) \}$ A) Yes B) No

Find the equation of the circle. Express the equation in standard form - A) $( x - 30 ) ^ { 2 } + ( y - 25 ) ^ { 2 } = 10 ^ { 2 }$ B) $( x - 30 ) ^ { 2 } + ( y + 25 ) ^ { 2 } = 10 ^ { 2 }$ C) $( x + 25 ) ^ { 2 } + ( y + 30 ) ^ { 2 } = 10 ^ { 2 }$ D) $( x - 25 ) ^ { 2 } + ( y - 30 ) ^ { 2 } = 5 ^ { 2 }$

Graph the equation. - $y = x ^ { 2 } + 6 x + 5$

Solve the problem. -Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with an embroidery of a Great Pyrenees dog on the front. There are fixed costs of $670 to set up for production, and variable costs of $44 per jacket. Write an equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x jackets. A) C(x) = 670x + 44 B) C(x) = 670 - 44x C) C(x) = 670 + 44x D) C(x) = (670 + 44) x

Use substitution to determine whether the given ordered pair is a solution of the given equation. -(4, 5); 5x + 3y = 35

Find the distance between the pair of points. Give an exact answer, and where appropriate, an approximation to three decimal places. - (7,4) and (9,8) A) $\sqrt { 12 } , 3.464$ B) $\sqrt { 20 } , 4.472$ C) $\sqrt { 40 } , 6.325$ D) $\sqrt { 4 } , 2.000$

Solve the problem. -In 1980, the population of a city was 5.5 million. By 1992 the population had grown to 6.5 million. Find the average rate of change in population from 1980 to 1992.. A) $\frac { 1 } { 9 } \text { million per year }$ B) $\frac { 1 } { 12 } \text { million per year }$ C) $\frac { 1 } { 14 } \text { million per year }$ D) $\frac { 13 } { 24 } \text { million per year }$

Graph the function. - $f ( x ) = 3 x - \frac { 1 } { 2 } x ^ { 3 }$ A) B) C) D)

Determine whether the pair of lines is parallel, perpendicular, or neither. -3x - 6y = 15 36x + 9y = 15