1.Eliminate the parameter t to find a Cartesian equation for: x=t^2 y=1+3t x=Ay^

Question

1.Eliminate the parameter t to find a Cartesian equation for:

x=t^2

y=1+3t

x=Ay^2+By+C

where
A =

and B =

and C =

2.Find the solution of the exponential equation

2e^x?7=3

in terms of logarithms, or correct to four decimal places.
x=

3.The graph of the function f(x)=log2(x?5) can be obtained from the graph of g(x)=log2x by one of the following actions: (a) shifting the graph of g(x) to the right 5 units; (b) shifting the graph of g(x) to the left 5 units; (c) shifting the graph of g(x) upward 5 units; (d) shifting the graph of g(x) downward 5 units; Your answer is (input a, b, c, or d)............?
The domain of the function f(x) is x>A, find A
The value of A is ...........?
Is the range of the function f(x) still (??,?)?
Your answer is (input Yes or No)..........?

4. Find the inverse function of f(x)=9x+7???????.
f^-1(x)...............?

5.Starting with the graph of f(x)=8^x, write the equation of the graph that results from

(a) shifting f(x) 8 units upward. y=

(b) shifting f(x) 8 units to the left. y=

(c) reflecting f(x) about the y-axis. y=

6.Express the function h(x)=1/(x?6) in the form f?g. If g(x)=x?6, find the function f(x).
Your answer is f(x)=..........?

7.Let f(x)=5x+3 and g(x)=5x^2+3x.
(fg)(2)=..............?

9.The domain of the function f(x)=7+6x?x^2???????????? is the closed interval [A,B] where A equals ...........?
and where B equals.......?

10.log4x+log4(x+1)=log4 4

x=

11.f logb2=x and logb3=y, evaluate the following in terms of x and y:

(a) logb54=

(b) logb36=

(c) logb881=

(d) logb81logb4=

12. If f(x)=8?7x, find f^-1(5).
Your answer is

Explanation / Answer

1. A=1/9

B= -2/9

C=1/9

2. x=2.8382

3. d

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