Exam 1: Graphs, Functions, and Models

Find the domain of the function. - $f ( x ) = \frac { x } { x - 3 }$ A) $\{ x \mid x < 0 \} , \text { or } ( - \infty , 0 )$ B) $\{ x \mid x \neq 3 \} , \text { or } ( - \infty , 3 ) \cup ( 3 , \infty )$ C) $\{ x \mid x \neq - 3 \} , \text { or } ( - \infty , - 3 ) \cup ( - 3 , \infty )$ D) $\{ x \mid x > 0 \} , \text { or } ( 0 , \infty )$

By graphing the function, visually estimate its domain and range. - $g ( x ) = x ^ { 2 } - 5$ A) $\text { Domain: } ( - \infty , \infty ) \text {; range: } ( - \infty , \infty )$ B) $\text { Domain: } [ 5 , \infty ) ; \text { range: } [ 5 , \infty )$ C) $\text { Domain: } ( - \infty , \infty ) \text {; range : } [ - 5 , \infty )$ D) $\text { Domain: } [ 5 , \infty ) ; \text { range: } ( - \infty , \infty )$

Solve the problem. -Find the average rate of change. A) 0.4 mph B) 0.2 mph C) 4.6 mph D) 2.6 mph

Find an equation for the circle. -Center at (5,-8) , diameter of length 6.2 A) $( x - 5 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 3.1$ B) $( x - 5 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 9.61$ C) $( x + 5 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9.61$ D) $( x + 5 ) ^ { 2 } - ( y + 8 ) ^ { 2 } = 38.44$

Solve the equation. -7x-(2 x-1)=2 A) $\frac { 1 } { 5 }$ B) $- \frac { 1 } { 9 }$ C) $\frac { 1 } { 9 }$ D) $- \frac { 1 } { 5 }$

Find the slope and the y-intercept of the line with the given equation. -x=11 A) not defined; no y-intercept B) not defined; (11,0) C) -11 ;(-11,0) D) -11 ;(0,0)

Find the distance between the pair of points. Give an exact answer, and where appropriate, an approximation to three decimal places. -(-1,9) and (-7,12) A) $\sqrt { 9 } , 3.000$ B) $\sqrt { 18 } , 4.243$ C) $\sqrt { 90 } , 9.487$ D) $\sqrt { 45 } , 6.708$

Find the slope and the y-intercept of the line with the given equation. - $f ( x ) = - \frac { 3 } { 5 } x + 1$ A) $- \frac { 3 } { 5 } ; ( 0,1 )$ B) $\frac { 3 } { 5 } ; ( 1,0 )$ C) -1 ;(0,1) D) 1 ;(0,1)

Find the domain of the function. - $f ( x ) = 6 - \frac { 4 } { x }$ A) $\{ x \mid x > 6 \} \text {, or } ( 6 , \infty )$ B) $\{ x \mid x < 4 \} \text {, or } ( - \infty , 4 )$ C) all real numbers, or $( - \infty , \infty )$ D) $\{ x \mid x \neq 0 \} \text {, or } ( - \infty , 0 ) \cup ( 0 , \infty )$

Determine whether a linear model might fit the data. - A) Yes B) No

Find the zero of the linear function. -f(x)=11-x A) -11 B) 11 C) 1 D) -22

Solve the problem. - $x ^ { 2 } + ( y + 9 ) ^ { 2 } = 16$

Solve the problem. -A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. By using linear regression, the following function is obtained: y = 88.6 - 1.86x where x is the number of hours spent in the lab and y is grade on the test. Use this function to predict the grade of a student who spends 19 hours in the lab. Number of hours spent in lab Grade (percent) 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51 A) 69.6 B) 57.1 C) 49.3 D) 53.3

Find the midpoint of the segment having the given endpoints. -(6,5) and (4,3) A) (10,8) B) (4,5) C) (5,4) D) (2,2)

Find the midpoint of the segment having the given endpoints. -(3,7) and (-4,8) A) $\left( \frac { 7 } { 2 } , - \frac { 1 } { 2 } \right)$ B) $\left( - \frac { 1 } { 2 } , \frac { 15 } { 2 } \right)$ C) (-1,15) D) (7,-1)

Find the slope and the y-intercept of the line with the given equation. -f(x)=-1.5+x A) 1; (0,-1.5) B) 1; (0,1.5) C) -1; (0,-1.5) D) 1 ; (-1.5,0)

Write an equation in slope-intercept form for the line shown. - A) y= x-2 B) y= -x+2 C) y= -x-2 D) y= x+2

Find the domain of the function. - $f ( x ) = x ^ { 2 } + 6$ A) $\{ x \mid x \neq - 6 \} , \text { or } ( - \infty , - 6 ) \cup ( - 6 , \infty )$ B) $\{ x \mid x > - 6 \} , \text { or } ( - 6 , \infty )$ C) $\{ x \mid x \geq - 6 \} \text {, or } [ - 6 , \infty )$ D) all real numbers, or $( - \infty , \infty )$

Solve the problem. -The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge of $35 for the repairman to come to the house, to which a charge of $22 per hour is added. Find an equation that can be used to determine the labor cost, C(x), of a repair that takes x hours. A) C(x) = (35 + 22) x B) C(x) = 35 - 22x C) C(x) = 22 + 35x D) C(x) = 35 + 22x

Find the coordinates of the points shown on the graph. - A) C: (-3,-6) , D: (4,-6) B) C: (-3,4) , D: (-6,2) C) C: (-3,4) , D: (2,-6) D) C: (4,10) , D: (-6,2)