2) Sketch the graph of the following function. State the domain of the function, identify any intercepts and test for symmetry. f ( x )=53 x +2 3) Suppose (3, - 4) is on the graph of y = f(x). Use Theorem 1.7 to find a point on the graph of the following transformed function. y=2 f ( x7 )+ 3 4) Find both the point-slope form and the slope-intercept form of the line with the given slope which passes through the given point. 2 m= , P=(5 ,10) 5 5) Find both the point-slope form and the slope-intercept form of the line with the given slope which passes through the given point. m=0, P=(50 , 100) 6) Find the slope-intercept form of the line which passes through the given points. P=(5 ,10 ) Q=(5 , 20) 7) A salesperson is paid $300 per week plus 4% commission on her weekly sales of x dollars. Find a linear function that represents her total weekly pay, W (in dollars) in terms of x. What must her weekly sales be in order for her to earn 475.00 for the week? 8) Solve the equation. 17|x| =3 5 9) Given the function. 1 f ( x )= |3 x1| 2 a) Graph the function b) Find the zeros of the above function c) Find the x- and y-intercepts of the above graph, if any exist. d) From the graph, determine the domain and range of the given function, e) List the intervals on which the function is increasing, decreasing or constant, and f) Find the relative and absolute extrema, if they exist. 10) Given the function f ( x )= |x +5| x +5 a) Graph the function b) Find the zeros of the above function c) Find the x- and y-intercepts of the above graph, if any exist. d) From the graph, determine the domain and range of the given function, e) List the intervals on which the function is increasing, decreasing or constant, and f) Find the relative and absolute extrema, if they exist. 1) Sketch the graph of the following function. State the domain of the function, identify any intercepts, and test for symmetry. f(x)=8-x2 Domain: ( , Intercepts The curve is symmetrical on y-axis 2) Sketch the graph of the following function. State the domain of the function, identify any intercepts and test for symmetry. f ( x )=53 x +2 Domain (-2, ) 3) Suppose (3, - 4) is on the graph of y = f(x). Use Theorem 1.7 to find a point on the graph of the following transformed function. y=2 f ( x7 )+ 3 4) Find both the point-slope form and the slope-intercept form of the line with the given slope which passes through the given point. 2 m= , P=(5 ,10) 5 Solution m=0.4 (Y-10) = 0.4 (x + 5) = 0.4x + 2 Point solution form: y - 10 = 0.4(x +5) Slope-intercept form: y = 0.4x +12 5) Find both the point-slope form and the slope-intercept form of the line with the given slope which passes through the given point. m=0, P=(50 , 100) Solution (y - 100) = 0 (x +50) Point solution form: Y-100= 0 Slope-intercept form: Y=100 6) Find the slope-intercept form of the line which passes through the given points. P=(5 ,10 ) Q=(5 , 20) Solution Finding gradient m = 20(10 ) 5(5 ) Slope-intercept form: y 10 =3 x5 Y+10=3x +15 =3 Y=3x+5 7) A salesperson is paid $300 per week plus 4% commission on her weekly sales of x dollars. Find a linear function that represents her total weekly pay, W (in dollars) in terms of x. What must her weekly sales be in order for her to earn 475.00 for the week? Solution Linear function: W=$300+0.04x Weekly sales if W= $475.00 475 = 300+0.04x 0.04x = 475-300 X= 4,375.00 8) Solve the equation. 17|x| =3 5 Solution 17 -x = 3*5 X=17-15 X=2 9) Given the function. Sketching the graph 1 f ( x )= |3 x1| 2 Finding zeros: 0.5(3x -1) = 0 X-intercept = ( 1 x= 3 1 ,0 3 Y-intercept = (0, -0.5) Domain: (, ) Increasing: none Decreasing: (0 , Relative and absolute extrema does not exist 10) Given the function f ( x )= |x +5| x +5 Intervals -5 > x > -5 Increasing (-5, ) Decreasing (-5,- ) Absolute extrema do not exist