Question 1 (essay worth 10 points)
(03.03 mc)
the table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −12
0 −6
1 0
g(x)
g(x) = 2x + 6
part a: write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
part b: which function has a greater y-intercept? justify your answer. (4 points)

Step-by-step explanation:

Both functions are linear, as the highest power of x is 1 in each case.

The function represented by the table has a slope of 6, since each unit increase in x results in a unit increase of 6 in y.

The function g(x) = 2x + 6 has a slope of 2.

The y intercept of f(x) is (0, -6), which we can read directly from the table.

The y int. of g(x) is 6, which can be read directly from y = 2x + 6.

g(x) has the greater y-intercept:  +6 versus -6.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places