1.) Use algebra correctly to simplify the difference quotient of a polynomial function.

Find and simplify the difference quotient for the function g(t)=5t/t+7.

The work starts with the difference quotient in the general form: f(x+h)-f(x)/h

2.) Find the domain of the function. f(x)=x+4 / 3x^2-x-4

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3.Find the domain of the function. i(x)=x^4+2x^3 / x^5-16x

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4.) Find the domain of the function. (Round each answer to three decimal place.) k(x)= 4/x^5+3x^4-3

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5.) Use algebra to determine the location of the vertical asymptotes and holes in the graph of the function. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) g(x)= 6x^2/ x^4-4x^2

x=

x=

x=

x=

6.) Analyze the function algebraically. List its vertical asymptotes, holes, y-intercept, and horizontal asymptote, if any. Then sketch a complete graph of the function. (If there is no answer, enter NONE in the answer box.)

q(x)=-1/ x-3

vertical asymptote=

hole x=

horizontal asymptote=

y-intercept: _______,_______

7. Analyze the function algebraically. List its vertical asymptotes, holes, y-intercept, and horizontal asymptote, if any. Then sketch a complete graph of the function. (If there is no answer, enter NONE in the answer box.)

6x^2/ (x+1)(x-2)

larger x-value-

smaller x-value-

hole- x=

horizontal asymptote y=

y-intercept=

8.) Analyze the function algebraically. List its vertical asymptotes, holes, y-intercept, and horizontal asymptote, if any. Then sketch a complete graph of the function. (If there is no answer, enter NONE in the answer box.)

f(x)= 5/(x+1)^2(x-2)

larger x-value-

smaller x-value-

hole- x=

horizontal asymptote y=

y-intercept=

9.) Analyze the function algebraically. List its vertical asymptotes, holes, y-intercept, and horizontal asymptote, if any. Then sketch a complete graph of the function. (If there is no answer, enter NONE in the answer box.)

f(x) = (x-1)(x-2)(x-3) / (4x+1)

larger x-value-

smaller x-value-

hole- x=

horizontal asymptote y=

y-intercept=