Name: Terri WoodardMTH133Unit 4 – Individual Project – AName: Terri Woodard1) State the domain of the following:a)Answer: x ? -4b)Answer: All real number excluding x = 7 (x ? 7)c)Answer: All real numberd)Answer: All real numbere)Answer: All real number2) Suppose the graph of is shifted to obtain each the following graphs.
What is the equation of the function, g(x), for each graph?a)Answer:b)Answer:3) Consider the following graph of y = f(x).Pa) If h(x) = f(x) + 2, what would the new coordinates of P be after the shift? Give answer in (x, y) form. Answer: (1, 2)b) If , what would the new coordinates of P be after the reflection? Give answer in (x, y) form. Answer: (-1, 0)4) Consider the function .a) Find h, the x-coordinate of the vertex of this parabola. Answer: h = -2 Show your work here: h = – (b/2a) = – (4/2) = -2Or alternatively,= = =à h = -2b) Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y. Fill in the following table.
Make sure your x-values are in increasing order in your table.Answer:xy-41-3-2h = -2-3-1-201c) Use MS Excel to graph the function by plotting the points found in the table in part b.Answer:5) Find the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.a)Horizontal: y = 2Horizontal asymptote at y = (numerator’s leading coefficient) / (denominator’s leading coefficient) = 2x/x = 2 [the degrees of numerator and denominator are same]Vertical: x = -2Putting denominator x + 2 = 0 à x = -2b)Horizontal: y = 0 (x-axis)The denominator (for x) degree is greater then numerator degree by one, therefore, horizontal asymptote will be y = 0)Vertical: x = ± 1Putting denominator àc)Horizontal: y = 2Vertical: x = -2d)Horizontal: y = 0 (x-axis)Vertical: x = 1