Sketch the graph of each function by transforming the graph of an appropriate function of the form

(a) Explain what is meant by $\lim _{x \rightarrow a} f(x)=L.$ (b) If $\lim _{x \rightarrow 2} f(x)=5,$ is it possible that f(2) = 3? (c) Find $\lim _{x \rightarrow 2} x^{2}.$

Which line would not be found in a truth table for or? a) T T T b) T F T c) F T F d) F F F

Every day Sandra chooses whether to wear green or brown flip-flops. How many possible ways could she choose her shoes over the course of 5 days?

A half-dollar has a diameter of about 31 millimeters. About how many millimeters long would a row of 56 half-dollars be?

(a) Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. a(t) = 12t i + sin(t) j + cos(2t) k, v(0) = i, r(0) = j

Use the Factor Theorem to show that the statement in the exercise is true. Show that x + 4 is a factor of the polynomial $P(x)=x^{5}+4 x^{4}-7 x^{3}-23 x^{2}+23 x+12$

True/False: a and (b or c) == (a and b) or (a and c)

Review the vocabulary words listed. Distinguish between the vocabulary words in each pair below. DNA replication, double helix, nitrogenous base, codon, messenger RNA, ribosomal RNA, transcription, transfer RNA, translation, chromosomal mutation, frameshift mutation, mutagen, mutation, point mutation. transcription—translation

Find the exact value. $\csc \frac{9 \pi}{4}$

(a) find the dot product $\mathbf{v} \cdot \mathbf{w}$; (b) find the angle between v and w; (c) state whether the vectors are parallel, orthogonal, or neither. $\mathbf{v}=\sqrt{3} \mathbf{i}-\mathbf{j}, \quad \mathbf{w}=\mathbf{i}+\mathbf{j}$

True/False: The statement myShape.move (10,20) moves myShape to the point (10,20).

Suppose that $f(x)=x^{2}+2 x-8$ What is the vertex of f ?

On the average, each human has about six recessive alleles that would be lethal if expressed. Why do you think that human cultures have laws against marriage between close relatives?