1314 Final Exam Review 1. For the given graph of the function f, find (a) Domain:

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1 114 Final Exam Review 1. For the given graph of the function f, find (a) Domain: (b) Range: (c) State the x intercept(s): (d) State the y intercept: (e) State the value of f ( 4): (f) State the intervals on which the function is increasing, if any. (g) State the intervals on which the function is decreasing, if any. (h) State the intervals on which the function is constant, if any. f ( xh) f( x). Given f( x) 4x x 5, find. (Simplify your answer) h. Given x x ( ) 4 find an equation of the secant line containing, f( ) and 1, f (1)

2 For the given quadratic function, find the vertex. Sketch the graph. Give the equation of the parabola s axis of symmetry. Find the intercepts and range of the function. 4. ( ) ( x1) 4 Vertex: Range: Axis of symmetry: y intercept: x intercept(s): 5. Graph the following functions. State the vertex, the domain, range and all intercepts. (a) f( x) x 1 (b) 1 f( x) x4

3 Solve and graph solution on a number line. Write answer in interval notation x 11x x 1x 5 8. Given: x x x ( ) ( 1) ( ) ( 5) (c) Find the x-intercepts: and state their multiplicity. (a) What is the leading term? (b) Describe the end (extreme) behavior of the graph. (d) Find the y-intercept: (e) Graph the function as shown in class. 9. Find the domain of the function. 1 a) f( x) 6x 5x4 b) hx ( ) 5 x

4 10. Use the Rational Zero Theorem (make a list of possible zeroes), the given graph, and synthetic division to find all zeros of each polynomial function. Show all work. (a) 4 ( ) x 5x 7x 5x15 (b) x x x 4 ( ) Find the intercepts and asymptotes algebraically. (a) f( x) x 1 x 9 (b) 4x 4 f( x) 1x 11x 15

5 SOLVE THE FOLLOWING INEQUALITIES. Write answers in interval notation. SHOW ALL WORK. 1. x x 1 1. x 1 4 x 5 GRAPH the following functions. 14. y x y x y x y 1 ( ) x x ( ) 1 4

6 19. Given and f( x) x x 7 and g( x) 4x 9 find the following. (a) ( f g)( x) (Simplify answer) (b) ( g f )( x) (simplify answer) 0. Find the inverse of the function. (a) ( ) ( x ) 1 (b) f( x) 5x 4 1. Graph the function and label one key point. Find the domain and range. Give equation of the asymptote. A B f( x) log ( x4) C x1 ( ) x ( ) 4 D f( x) ln( x) 1

7 Solve each equation. Where necessary, round to the nearest thousandth. (Decimal part is optional). x x 4 14 e x 5e 1 1 log( x4) log( x ) 1 6. log (4x10) log ( x 1) log (x) log xlog ( x ) 8. log ( x5) log ( x ) log( x 1) log( x 5)

8 0. Complete the square and write the equation of the circle in standard form. (Simplify all radicals) a) x y x y b) x y x y Perform the given row operation for the following matrix R R R. Perform the given row operation for the following matrix R R R

9 114 Final Exam Review 1. For the given graph of the function f, find (a) Domain: (b) Range: (c) State the x intercept(s): (d) State the y intercept: (e) State the value of f ( 4): (f) State the intervals on which the function is increasing, if any. (g) State the intervals on which the function is decreasing, if any. (h) State the intervals on which the function is constant, if any. f ( xh) f( x). Given f( x) 4x x 5, find. (Simplify your answer) h. Given x x ( ) 4 find an equation of the secant line containing, f( ) and 1, f (1)

10 For the given quadratic function, find the vertex. Sketch the graph. Give the equation of the parabola s axis of symmetry. Find the intercepts and range of the function. 4. ( ) ( x1) 4 Vertex: Range: Axis of symmetry: y intercept: x intercept(s): 5. Graph the following functions. State the vertex, the domain, range and all intercepts. (a) f( x) x 1 (b) 1 f( x) x4

11 Solve and graph solution on a number line. Write answer in interval notation x 11x x 1x 5 8. Given: x x x ( ) ( 1) ( ) ( 5) (c) Find the x-intercepts: and state their multiplicity. (a) What is the leading term? (b) Describe the end (extreme) behavior of the graph. (d) Find the y-intercept: (e) Graph the function as shown in class. 9. Find the domain of the function. 1 a) f( x) 6x 5x4 b) hx ( ) 5 x

12 10. Use the Rational Zero Theorem (make a list of possible zeroes), the given graph, and synthetic division to find all zeros of each polynomial function. Show all work. (a) 4 ( ) x 5x 7x 5x15 (b) x x x 4 ( ) Find the intercepts and asymptotes algebraically. (a) x 1 f( x) x 9 (b) 4x 4 f( x) 1x 11x 15

13 SOLVE THE FOLLOWING INEQUALITIES. Write answers in interval notation. SHOW ALL WORK. 1. x x 1 1. x 1 4 x 5 GRAPH the following functions. 14. y x y x y x y 1 ( ) x x ( ) 1 4

14 19. Given and f( x) x x 7 and g( x) 4x 9 find the following. (a) ( f g)( x) (Simplify answer) (b) ( g f )( x) (simplify answer) f(4x9) (4x9) (4x9) 7 g x x x x (16x 7x81) 8x18 7 1x 8x8 9 48x 16x4 8x5 1x 8x 7 48x 08x Find the inverse of the function. (a) f( x) ( x ) 1 (b) f( x) 5x 4 x x1 ( y) ( y ) 1 x1 ( y) x1 ( y) x 1 1 ( ) ( 7) 4( 7) 9 5y4 1. Graph the function and label one key point. Find the domain and range. Give equation of the asymptote. x x 5y4 x 5y4 x 45y x 4 f 5 1 ( x) A B f( x) log ( x4) C x1 ( ) x ( ) 4 D: (, ) R: (, ) A: y D: (4, ) R: (, ) A: x 4 D: (, ) R: (,4) A: y 4 D f( x) ln( x) 1 D: (, ) R: (, ) A: x

15 . x x 4 14 e x 5e 1 1 log ( x4) log ( x ) 1 6. log (4x10) log ( x 1) log (x) log xlog ( x ) 8. log ( x5) log ( x ) log ( x 1) log ( x 5)

16 0. Complete the square and write the equation of the circle in standard form. (Simplify all radicals) a) x y x y b) x y 8x y Perform the given row operation for the following matrix R R R. Perform the given row operation for the following matrix R R R

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