MATH 101 Precalculus Tutorial 7 October 2024 PDF

Botswana International University of Science and Technology (BIUST) Department of Mathematics and Statistical Sciences MATH 101 Precalculus Tutorial 7. October 2024 Question 1. Suppose the graph of y = f (x) is given. Determine how the graph of each fun...

Botswana International University of Science and Technology (BIUST) Department of Mathematics and Statistical Sciences MATH 101 Precalculus Tutorial 7. October 2024 Question 1. Suppose the graph of y = f (x) is given. Determine how the graph of each function below can be obtained from the graph of y = f (x). 1 (a) y = f (x) − 1 (b) y = f (x + 5) (c) y = f (x) (d) y = f (x − 5) + 2. 3 Question 2. Consider the quadratic function f (x) = 5x2 − 30x + 49. (a) Express f in the standard form, i.e f (x) = a(x − h)2 + k. (b) Determine the direction of opening of the graph. (c) Find the turning point (vertex) of the graph. (d) Determine the minimum value of f. (e) Determine the x− and y− intercepts if any. (f) Sketch the graph of f. Question 3. Find the maximum or minimum value of each of the following quadratic functions 1 (a) g(x) = −2x2 + 4x − 5 (b) h(x) = x2 + 2x − 6 (c) g(x) = 2x2 − 4x − 7 2 Question 4. Find the partial fraction decomposition of: x3 + 2x2 + 61 2x3 + 11 5x2 − 2x − 1 x(x + 3) (a) (b) (c) (d) (x + 3)2 (x2 + 4) (x2 + 4)(x − 3) (x + 1)(x2 + 1) x2+ x − 12 −2x2 + 5x − 1 x 7x − 3 x5 − 2x4 + x3 + x + 5 (e) (f) (g) (h). x4 − 2x3 + 2x − 1 2 8x − 10x + 3 x + 2x2 − 3x 3 x3 − 2x2 + x − 2 Question 5. Find the intercepts, minimum or maximum value and the range for the following func- tions. Also sketch the graph. (a) f (x) = −2x2 + 5x + 3 (b) f (x) = x2 + 2x + 3 (c) y = 5x2 + 26x + 5 Question 6. Use the graph of the function f (x) = x2 to graph the following functions: (a) p(x) = 2x2 + 3 (b) g(x) = x2 + 1 (c) g(x) = −x2 (d) g(x) = (x + 1)2