For any exponential function, f(x) = abx, the range is the set of real numbers above or below the horizontal asymptote, y = d, but does not include d, the value of the asymptote.
Overall, the steps for algebraically finding the range of a function are:
Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
Find the domain of g(y), and this will be the range of f(x).
If you can't seem to solve for x, then try graphing the function to find the range.
(a) Using the completing the square method, we need to write into the form of where , so
Expand to find the value of c
Notice that we get back the first two terms, the and the .We need to get rid of the last term of '9' as the term was not in the original form. The final form will look like
Hence,
(b)
(c) , square root both sides plus and minus of 2 Hence
Look at points (0, -1) and (1, 5).
m = (y2 - y1)/(x2 - x1) = (5 - (-1))/(1 - 0) = 6/1 = 6
Slope = 6
Answer: 6
Answer:14
Step-by-step explanation: minus *minus = + so its +27
and then you just do the maths 27-13=14
