Exam 1: Graphs, Functions, and Models

Find the equation of the circle. Express the equation in standard form - A) $( x - 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1 ^ { 2 }$ B) $( x + 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1 ^ { 2 }$ C) $( x + 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 1 ^ { 2 }$ D) $( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 1 ^ { 2 }$

Evaluate as requested. -Given that $f ( x ) = x ^ { 2 } - 4 x + 3 , \text { find } f ( - 2 )$ A) -7 B) 9 C) -1 D) 15

Find an equation for the circle. -Center (22, 24), containing the origin A) $( x - 24 ) ^ { 2 } + ( y - 22 ) ^ { 2 } = 1060$ B) $( x - 22 ) ^ { 2 } + ( y - 24 ) ^ { 2 } = 33$ C) $( x - 24 ) ^ { 2 } + ( y - 22 ) ^ { 2 } = 33$ D) $( x - 22 ) ^ { 2 } + ( y - 24 ) ^ { 2 } = 1060$

Solve the problem. -The function H described by H(x) =2.75x+71.48 can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose humerus is 33.8 cm long. A) 40.43 cm B) 164.43 cm C) 108.03 cm D) 21.47 cm

Find the distance between the pair of points. Give an exact answer, and where appropriate, an approximation to three decimal places. -(0, 0) and (x, y) A) $x ^ { 2 } + y ^ { 2 }$ B) $\sqrt { x ^ { 2 } + y ^ { 2 } }$ C) $\sqrt { x + y }$ D) x+y

Solve the problem. -A deep sea diving bell is being lowered at a constant rate. After 12 minutes, the bell is at a depth of 500 feet. After 55 minutes the bell is at a depth of 1400 feet. What is the average rate of lowering per Minute? Round your answer to the nearest tenth.

Find the slope of the line containing the given points. -f(8.3)= 6.5 and f(-11.6)=-7.9 A) $- \frac { 144 } { 199 }$ B) $\frac { 199 } { 144 }$ C) $- \frac { 199 } { 144 }$ D) $\frac { 144 } { 199 }$

Solve the equation. --23=-6 x-5 A) 3 B) -8 C) 8 D) -12

Find the zero of the linear function. - f(x)=-4 x+5 A) -1 B) 1 C) $\frac { 5 } { 4 }$ D) $- \frac { 4 } { 5 }$

Evaluate as requested. -Given that $g ( x ) = 5 x ^ { 3 }$ find g(5+h) . A) $625 - 375 h + 50 h ^ { 2 } - 5 h ^ { 3 }$ B) $125 + 75 h + 75 h ^ { 2 } + 6 h ^ { 3 }$ C) $- 625 + 375 h - 15 h ^ { 2 } + h ^ { 3 }$ D) $625 + 375 h + 75 h ^ { 2 } + 5 h ^ { 3 }$

Solve the problem. -Roberto invested some money at 8%, and then invested $3000 more than twice this amount at 11%. His total annual income from the two investments was $4830. How much was invested at 11%?

Find an equation for the circle. -Center at (0,-5) , radius 9 A) $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$ B) $( x - 5 ) ^ { 2 } + y ^ { 2 } = 81$ C) $x ^ { 2 } + ( y + 5 ) ^ { 2 } = 81$ D) $( x + 5 ) ^ { 2 } + y ^ { 2 } = 81$

Write a slope-intercept equation for a line with the given characteristics. -Passes through (-5,-9) and (0,-2) A) $y = - \frac { 7 } { 5 } x - 2$ в) $y = \frac { 7 } { 5 } x - 2$ C) y=2 x-2 D) y=-2 x-2

Solve the problem using your calculator. -Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained Regarding their GPAs on entering the program versus their current GPAs. Use a graphing Calculator to model the data with a linear function that predicts a student's current GPA as a Function of his or her entering GPA. Entering GPA Current GPA 3.5 3.6 3.8 3.7 3.6 3.9 3.6 3.6 3.5 3.9 3.9 3.8 4.0 3.7 3.9 3.9 3.5 3.8 3.7 4.0 A) y=2.51+0.329x B) y=5.81+0.497 x C) y=3.67+0.0313 x D) y=4.91+0.0212 x

Determine the slope, if it exists, of the graph of the given linear equation. - $y = \frac { 1 } { 3 }$ A) m= $\frac { 1 } { 3 }$ B) m=0 C) not defined D) m= $- \frac { 1 } { 3 }$

Use substitution to determine whether the given ordered pair is a solution of the given equation. -(-4, -22); y = 5x - 2

Find the domain of the function. - $f ( x ) = \frac { 1 } { x ^ { 2 } + 5 x - 14 }$ A) $\{ x \mid x \neq - 7 \text { and } x \neq 2 \} , \text { or } ( - \infty , - 7 ) \cup ( - 7,2 ) \cup ( 2 , \infty )$ B) $\{ x \mid x \neq - 7 \} \text {, or } ( - \infty , - 7 ) \cup ( - 7 , \infty )$ C) $\{ x \mid x \neq 2 \} , \text { or } ( - \infty , 2 ) \cup ( 2 , \infty )$ D) all real numbers, or $( - \infty , \infty )$

Graph the equation using the slope and the y-intercept. - A) B) C) D)

Find the domain and range of the function represented in the graph. - A) Domain: $[ - \pi , 2 \pi ]$ Range: [-3,3] B) Domain: $[ 0,2 \pi ]$ Range: [0,3] C) Domain: $[ \pi , 2 \pi ]$ Range: [-4,2] D) Domain: [-3,3] ; Range: $[ - \pi , 2 \pi ]$

Solve the problem. -A salesperson has two job offers. Company A offers a weekly salary of $280 plus commission of 14% of sales. Company B offers a weekly salary of $560 plus commission of 7% of sales. What is the amount of sales above which Company A's offer is the better of the two?