Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Assignment #1 – Functions

MAT A29 Calculus I for the Life Sciences – Dr Parker Glynn-Adey

Learning Objectives

● Investigate quantitative relationships using graphs, their domains, and ranges.

1. Find an equation of the form y = mx + b with x-intercept x = −6 and y-intercept y = 9.

2. Consider the function f(x) = .

(a) Find the domain of f(x).

(b) Find the range of f(x).

(c) Find the x and y intercepts of y = f(x), if they exist.

3. Consider the function f(x) = .

(a) Find the domain of f(x).

(b) Find the range of f(x).

(c) Find all x and y intercepts of f(x), if they exist.

4. Consider the functions f(x) = and g(x) = x + 9.

(a) Find the domain of (f ○ g)(x).

(b) Find the domain of (g ○ f)(x).

5. Consider the polynomial p(x) = −3x² + 6x.

(a) Write the degree of the polynomial, no explanation is needed.

(b) Use the leading coefficient to determine the behaviour of p(x) for large values of x

(c) Find the zeroes of the polynomial, explain your method for solving the polynomial.

(d) Explain whether the polynomial p(x) is even, odd, or neither.

6. Sketch the function f(x) given below. Label the point where the pieces of the pieceswise function meet.