1) The line has a slope of ) The line passes through (2, 11) and. 6) r(x) = x + 4. From memory match each equation with its graph.

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1 Review Test 2 Math 1314 Name Write an equation of the line satisfying the given conditions. Write the answer in standard form. 1) The line has a slope of and contains the point (3, 1). Use the point-slope formula to write an equation of the line that passes through the given points. Write the answer in slope-intercept form (if possible). 2) (3, 2) and (-3, -3) Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. 3) The line passes through (-6, 9) and (-6, -15). 4) The line passes through (2, 11) and (11, 11). From memory match each equation with its graph. 5) f(x) = x g(x) = 1 x I II III h(x) = x 3 Sketch the graph using transformations of a parent function (without a table of values). 6) r(x) = x + 4 Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients. 7) Passes through (-5, -1) and is parallel to the line defined by 3x - 5y = 9 Sketch the graph using transformations of a parent function (without a table of values). 8) a(x) = (x - 1) 2 Use transformations to graph the given function. 9) f (x) = 2x 10) f(x) = 4x 3 1

2 Graph the function by applying an appropriate reflection. 11) f(x) = - x Graph the equation by plotting points. 12) p(x) = (-x) 3 Use the graph of y = f (x) below to graph y = f (-x) 13) Evaluate the function for the given value of x. 18) f (x) = 5x, g(x) = -4x 2-7, (g - f )(x) =? Find f(-x) and determine whether f is odd, even, or neither. 19) f (x) = -5x 5 + 4x 3 Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. 20) Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients. 14) Passes through (1, -5) and is perpendicular to the line defined by -3x + 4y = 6 Evaluate the function for the given value of x. 15) f (x) = x 2 + 2x, g(x) = 5x - 1, (g f )(2) =? 16) f (x) = -2x, g(x) = x + 1, (f g)(-4) =? Find the indicated function and write its domain in interval notation. 17) m(x) = x + 4, n(x) = x - 3, (m n)(x) =? Graph the function. -x - 3 for x -3 21) s(x) = x + 3 for x > -3 Find the indicated function and write its domain in interval notation. 22) n(x) = x - 2, p(x) = x 2-9x, (p n)(x) =? Determine whether the graph of the parabola opens upward or downward and determine the range. 23) f (x) = -2(x + 1) Identify the vertex and determine the minimum or maximum value of the function. 24) f (x) = 2(x + 3) 2-4 2

3 Graph the function and determine the minimum or maximum value of the function. 25) m(x) = 2(x - 2) 2 Sketch the function and determine the axis of symmetry. 26) f (x) = -(x + 2) Determine the x- and y-intercepts for the given function. 27) f (x) = -2(x + 4) Identify the location and value of any relative maxima or minima of the function. 28) Evaluate the function for the indicated value. 32) Evaluate f (-3). f (x) = 10 x -3 x < x 2-5 x > 2 Identify the vertex, axis of symmetry, and intercepts for the graph of the function. 33) g(x) = x 2-2x - 8 Find the vertex of the parabola by applying the vertex formula. 34) f (x) = 1 4 x2 + 6x - 1 Determine the end behavior of the graph of the function. 35) f (x) = -x 2 (7 - x)(3x + 8) 4 Find the zeros of the function and state the multiplicities. 36) f (x) = -2x 4-17x 3-36x 2 37) f (x) = -5x(4x - 5)(5x - 6)(x + 5)(x - 5) List the possible rational zeros. 29) f (x) = -49x 4 + 5x 3 + 7x + 14 Use the remainder theorem to determine if the given number c is a zero of the polynomial. 30) x 4 + 9x x 2-15x + 20; c = 5 Determine the number of possible positive and negative real zeros for the given function. 31) f (x) = -8x 7-2x 4 + 4x 3 + 5x 2 + 7x + 5 Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval. 38) f (x) = x 3-2x x + 28; [4, 5] Sketch the function. 39) f (x) = x 3 + 2x 2 Use synthetic division to divide the polynomials. 40) 2x5-6x 4-15x x 2-71x + 26 x - 2 3

4 A polynomial f (x) and one of its zeros are given. Factor f (x) as a product of linear factors. 41) f (x) = 5x 3-41x x - 32; 4-4i is a zero Use synthetic division to divide the polynomials. 42) x5-243 x - 3 4

5 1) 2x + 7y = 13 2) y = 5 6 x ) x = -6 4) y = 11 5) f(x), I; g(x), III; h(x), II 6) 7) 3x - 5y = -10 8) 5

6 9) 10) 11) 6

7 12) 13) 14) 4x + 3y = ) (g f )(2) = 39 16) (f g)(-4) = 24 17) (m n)(x) = x + 1; domain: [-1, ) 18) (g - f )(x) = -4x 2-5x ) f (-x) = 5x 5-4x 3 ; f is odd. 20) a. (-, -3) (1, ) b. never decreasing c. (-3, 1) 7

8 21) 22) (p n)(x) = x 2-13x + 22; domain (-, ) 23) Downward Range: (-, 4] 24) Vertex: (-3, -4) Minimum: -4 25) minimum value = 0 8

9 26) Axis of symmetry: x = -2 27) x-intercepts: (-6, 0) and (-2, 0) y-intercept: (0, -24) 28) At x = -4, the function has a relative minimum of -5. At x = 0, the function has a relative maximum of 0. At x = 4, the function has a relative minimum of ) ±1, ± 1 7, ± 1 49, ±7, ±2, ±14, ±2 7, ± ) No 31) Positive: 1; Negative: 4 or 2 32) 10 33) Vertex at (1, -9); axis: x = 1; x-intercepts: (-2, 0) and (4, 0); y-intercept: (0, -8) 34) (-12, -37) 35) Down left and up right 36) 0 (multiplicity 2), -4 (multiplicity 1), (multiplicity 1) 37) 0, 5 4, 6, ± 5 ; each of multiplicity ) No 9

10 39) 40) 2x 4-2x 3-19x x ) (5x - 1)(x - (4-4i))(x - (4 + 4i)) 42) x 4 + 3x 3 + 9x x