Question 1Write a system of two equations with exactly one s

Question: 1)Write a system of two equations with exactly one solution. Show this graphically and algebraically.

2) Write a system of two equations with no solutions. Show this graphically and algebraically.

3) Write a system of two equations with exactly two solutions. Show this graphically and algebraically.

4)Write the equation for a logarithmic function that passes through the point (2,5). Graph This function.

5) Write the equation for an exponential function that passes through the point (1,7). Graph This function.

6)Write the equation for a hyperbola that passes through the point ( 2, 3)

7) Write the equation for a function with a horizontal asymptote. Graph this function. Algebraically prove the existence of the asymptote.

8) Write the equation for a function with a vertical asymptote. Graph this function. Algebraically prove the existence of the asymptote.

9)Write the equation for a function with two vertical asymptotes. Graph this function. Algebraically prove the existence of the asymptotes.

10) Write the equation for a function with a horizontal symptomatic. Graph this function. Algebraically prove the existence of the asymptote.

11)Algebraically prove the following two equations are equal: Y= H.10^log(M)x Y= H. e^ln(M)x

12)Graph a function of your choice. Graph its inverse

13) Using algebra techniques, find the inverse of f(x)= (x-3)⁴ +4 . Plot both functions to demonstrate that they are inverses.

1.x+y=2

x-y=-3

adding them we get 2x=5

x=5/2

plugging back x=5/2 in any of the equation

y=2-5/2=-1/2

2. x+y=2, x + y= 4

Subtracting these equations we get

0= -2

Here we have no solutions