Choose the word from each commonly confused pair that correctly completes each sentence. The rusty fire escape did not look like it could (bare/bear) the weight of a small child.

In this problem, for the polynomial function f:

f(x)=(x-1)$^2$(x-3)(x+1)

(a) Find the x - and y-intercepts of f.

(b) Determine whether the graph of $f$ crosses or touches the $x$-axis at each $x$-intercept.

(c) End behavior: find the power function that the graph of $f$ resembles for large values of $|x|$.

(d) Determine the maximum number of turning points on the graph of $f$.

(e) Use the $x$-intercept(s) to find the intervals on which the graph of $f$ is above and below the $x$-axis.

(f) Plot the points obtained in the first and previous parts, and use the remaining information to connect them with a smooth, continuous curve.

Find the second, fourth, and eleventh terms of the sequence described by the explicit formula.

$$A(n)=11 \cdot(2)^{n-1}$$

For each recursive formula, find an explicit formula that represents the same sequence. $A(n)=A(n-1)+3 ; A(1)=4$

Write the binomial expansion for each expression.

$$(a-b)^7$$

Find $\frac{d y}{d x}$ in two ways: (a.) By implicit differentiation of the equation. (b.) By differentiating an explicit formula for y.

$$x y-x=y+2$$

In this problem, for the polynomial function f:

f(x)=(x+1)(x+4)(x-3)

(a) Find the x - and y-intercepts of f.

(b) Determine whether the graph of $f$ crosses or touches the $x$-axis at each $x$-intercept.

(c) End behavior: find the power function that the graph of $f$ resembles for large values of $|x|$.

(d) Determine the maximum number of turning points on the graph of $f$.

(e) Use the $x$-intercept(s) to find the intervals on which the graph of $f$ is above and below the $x$-axis.

(f) Plot the points obtained in the first and previous parts, and use the remaining information to connect them with a smooth, continuous curve.

Find the coefficient a of the given term in the expansion of the binomial. Binomial $(2 x-3 y)^{8}$ Term $a x^{4} y^{4}$

Write a possible explicit rule for the nth term of each sequece.
3, 6, 11, 18, 27, ...

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed. Choose four numbers that have the largest possible standard deviation.

Using matrix multiplication find the reflection of $(-1,2)$ about the $y$-axis

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed. Choose four numbers that have the smallest possible standard deviation.

Use straight-line depreciation to complete the yearly depreciation column of a depreciation schedule. Round answers to the nearest cent.

$$\begin{array}{} \text{Total cost}&\text{ Salvage value}&\text {Expected life}&&\text{ Yearly depreciation}\\ \$7,200& \$ 300 &3\text{years} \end{array}$$

How do algae differ from bacteria? From fungi?