Describe the reflection that transforms f(x) to g(x).
The graph of f(x) is transformed to obtain the graph of g(x) = 4f(3x + 21) - 15. Describe the horizontal translation that occurs.
Describe, in the appropriate order, the transformations that must be applied to the graph of f(x) to obtain the graph of g(x) = 5f(x - 9) + 7.
State the restrictions on X in the
expression \displaystyle
\frac{(x + 7)(x -1)}{(x -4)(x + 7)}
.
If a function is defined by a set of points, then the inverse can be found by
A. reflecting the points in the y-axis
B. interchanging the x- and y-coordinates
C. reflecting the points in the origin
D. taking the reciprocal of each coordinate
Are \displaystyle
\frac{6x^2 -27x - 105}{x - 7}
and \displaystyle
(x + 3)(x + 10)-(x+ 3)(x+ 5)
equivalent expressions? Justify your answer.
Sketch the inverse of given f(x).
Simplify the expression and state any restrictions.
\displaystyle
\frac{x - 8}{x + 7} \times \frac{x+ 15}{x^2 + 12x -45}
Simplify the expression and state any restrictions.
\displaystyle
\frac{x^2 +12x + 20}{x + 5} \div \frac{x^2 + 7x - 30}{x + 10}
Simplify the expression and state any restrictions.
\displaystyle
\frac{x + 3}{x - 7} - \frac{x+ 9}{x -2}
Simplify the expression and state any restrictions.
\displaystyle
\frac{x+ 8}{x + 3} + \frac{x - 6}{x^2 + 9x + 18}
a) Given the function g(x) = 4(3x+ 6)^2 + 9, identify the base function as one of f(x) = x, f(x) = x^2,
f(x) = \sqrt{x}, and f(x) = \frac{1}{x}.
b) Describe, in the appropriate order. the transformations that must be applied to the base function f(X) to obtain the transformed function g(X].
c) Sketch the graphs of f(x) and g(x).
d) State the domain and range of the functions.
a) Given the function \displaystyle
g(x) = \frac{1}{5}\sqrt{2(x- 8)}-3
, identify the base function as one of f(x) = x, f(x) = x^2, f(x) = \sqrt{x}, and f(x) = \frac{1}{x}.
b) Describe, in the appropriate order, the transformations that must be applied to the base function f(X] to obtain the transformed function g[X].
c) Sketch the graphs of f(x) and g(x).
d) State the domain and range of the functions.
Given the function g(x) = \frac{2}{0.5x} + 5, identify the base function as one of f(x) = x, f(x) = x^2, f(x) = \sqrt{x}, and f(x) = \frac{1}{x}.
b) Describe, in the appropriate order, the transformations that must be applied to the base function f(x) to obtain the transformed function g(x).
c) Sketch the graphs of f(x) and g(x).
d) State the domain and range of the functions.
For each function,
- i) determine
f^{-1}(x) - ii) graph
f(x)and its inverse - iii) determine whether the inverse of
f(x)is a function
\displaystyle
f(x) = 3x + 8
For each function,
- i) determine
f^{-1}(x) - ii) graph
f(x)and its inverse - iii) determine whether the inverse of
f(x)is a function
\displaystyle
f(x) = 6(x - 9)^2 + 8
A small skateboard company is trying to determine the best price for its boards. When the boards are priced at $80, 120 are sold in a month. After doing some research, the company finds that each increase of $5 will result in selling 15 fewer boards.
a) Write an equation to represent the revenue, R, in dollars, as a function of x, the number of $5 increases.
b) State the domain and range of the revenue function.
c) Determine the inverse of the revenue function. What does this equation represent in the context of the question? State the domain and range of the inverse.
d) Determine the number of $5 increases for a revenue of $8100.
A small plane is travelling between Windsor and Pele’e Island (a distance of approximately 60 km) and is directly affected by the prevailing winds. Thus, the actual speed of the plane with respect to the ground is the speed of the plane (160 km/h) plus or minus the wind speed, w.
a) Develop a simplified equation for the total time it takes to make a round trip if the wind speed is w. State the domain and range and any restrictions on this relationship.
b) Graph your relationship from part a).
c) The pilot thinks that if he has a strong headwind on the way out, then he will be able to make up any lost time on the way back when he has a tailwind. Determine if he is correct.
In Canada, fuel efficiency, l, for cars is stated in litres per 100 km. In the United States, fuel efficiency, m, is stated in miles
per gallon (mpg). The formula m = 235/l can be used to convert from the Canadian system to the United States system.
a) Sketch the graph of the function.
b) In Canada, cars that have better fuel efficiency have a lower value for 8. Is the same true for m? Justify your
response.