What is the period and horizontal phase shift of the function  $y=\csc\left(\frac{1}{10}\pi x-11\right)+2$y=csc(110 πx−11)+2 ?

The expression 8log_k(⁵√k)^p can be written as which of the following? 40p p8log_k(k/5) (8/5)^p or (8p)/5

Which statement must be true for  $f\left(x\right)=\log_{\frac{1}{2}}x$ƒ (x)=log₁₂ x when x₂ > x₁?

If  $\log_8x=\frac{4}{3}y$log₈x=43 y then the expression  $\log_2\left(64x^6\right)$log₂(64x⁶) can be rewritten as:  $\log_2\left(64x^6\right)=a+by.$log₂(64x⁶)=a+by. What are the values for a and b?

Amy's garage door code consists of 4 digits. The code allows any of the digits 0 through 9 inclusive, but the last digit must not be a 1.

The difference between the number of codes that are possible if repeats are allowed and the number of codes that are possible if repeats are not allowed is ___

X-3 and x+1 are both factors of the polynomial mx³-4x²+nx-6. Determine the values for both m and n.

Log₁₂₅X=2/3

Show that P(x)/x-a = Q(x)+ R/x-a can be rearranged to P(x)= Q(x)(x-a)+R

the zeros of p(x)=x⁴+3x³-15x²-19x+30

question 1.

- For function f

-the graph of y=f(x) extends down into quadrant lll and down into quadrant IV

-the zeros of f are -2,3 and 5 

-the degree of f<5

1.what degrees is possible for f?

2.what are the maximum and minimum multiplicities possible for a zero of f?

3.two possible equations?

4.two possible graphs of y=f(x)

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question 2.

a.show that p(x)/x-a=Q(x)+R/x-a can be rearranged to p(x)=Q(x)(x-a)+R

b.evaluate p(a),showing it simplifies to R.

c.how does the answer in part b. relate to the remainder theorem?

d.using p(x)=Q(x)(x-a)+a to explain the factor theorem.(hint:what is the value of R if there is no remainder? substituted this value for R into Q(x)(x-a)+R to show x-ais a factor of p(x).

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quastion 3

a cube with side length x has been modified by adjusting its side length x has been modified by adjusting its length, width and height. A student determined a function of the form v(x)=(x+a)(x+b)(x+c) can be used to represent the volume of the new box for different values of x, and then she graphed the function.

a.based on the graph ,predict how the side lengths of the original cube changed.(hint:what do the zeros of the function represent?

b.determine a polynomial function of the form v(x)=(x+a)(x+b)(x+c) that's matches the function in the graph .

c.which parts of the graph are realistic?(hint:all sides must be positive.using two negative side lengths to give positive volume is not realistic.)