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Term Test #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.

● Evaluate limits numerically, visually, and algebraically.

● Apply the rules of differentiation to algebraic and transcendental functions.

1. Consider the function .

(a) Find the domain of .

(b) Find the range of .

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

2. Use the following grid to sketch a function with domain and range . Your function must also satisfy:

You do not need to give a formula for your function to answer this question.

3. Consider the function shown in the graph below.

(a) For this part, no explanation is needed. Use the graph to calculate the limits:

(b) For this part, no explanation is needed. Use the graph to calculate the limits:

(c) Carefully answer, with explanation, the following question: For what values T does the following limit exist?

4. Consider the following limit:

(a) Explain why direct substitution of x = 6 gives an invalid answer.

(b) Calculate the limit, carefully explaining each step of the calculation.

5. (a) Sketch the following function:

Label all the interesing points of the graph including x-intercepts and y-intercepts and ends of lines.

(b) For each line in your sketch, label it with its slope.