Write the vertical reflection of the graph of y = f \left( x \right) across the x-axis using function notation.
Each of the following points A, lie on the curve y =f\left(x \right). State the coordinates of point A', the location of point A following the reflection y =-f\left(x \right).
For each of the following graphs of f \left( x \right), sketch the graph of -f \left( x \right):
The graph of y = P \left(x\right) is shown:
Sketch the graph of y = - P \left(x\right).
Consider the cubic function y = \left(x + 3\right) \left(x - 2\right) \left(x - 5\right).
Determine the x-intercepts.
A second cubic function has the same x-intercepts, but is a reflection of the original function across the x-axis. State the equation of the reflected function.
For each of the following functions f \left( x \right) and its corresponding graph:
f \left( x \right) = x^{2} + 3
f \left( x \right) = \left(x - 5\right)^{2}
f \left( x \right) = 2 x + 2
f \left( x \right) = \left| 3 x - 12\right|
f \left( x \right) = x^{3} + 2
The graph of a function f \left( x \right) is shown:
State the domain of f \left( x \right).
State the range of f \left( x \right).
Sketch the graph of the reflection - f \left( x \right).
State the domain of the reflected function -f \left( x \right).
State the range of the reflected function - f \left( x \right).
Consider the function f \left( x \right) = 3 x^{2}.
State the domain of f \left( x \right).
State the range f \left( x \right).
Sketch the result of reflecting f \left( x \right) across the x-axis:
State the domain of the reflected function.
State the range of the reflected function.
Write down anything you notice about the domain and range of a function when it is reflected across the x-axis.
Write the horizontal reflection of the graph of y = f \left( x \right) across the y-axis using function notation.
Each of the following points A, lie on the curve y =f\left(x \right). State the coordinates of point A', the location of point A following the reflection y =f\left(-x \right).
Consider the given graph of f \left( x \right):
Sketch the graph of f \left( - x \right).
What do you notice about the graphs of f \left( x \right) and f \left( -x \right). Explain why this is.
The graph of y = P \left(x\right) is shown. Sketch the graph of y = P \left( - x \right).
Consider the given graph of the function f \left( x \right) = \dfrac{1}{x + 6} - 3.
State the equations of the asymptotes of f \left( x \right).
For the related function f \left( - x \right), state the equations of the asymptotes.
Sketch the graph of the function f \left( - x \right).
Consider the function f \left( x \right) = \dfrac{3}{x + 1}.
State the domain of f \left( x \right).
State the range of f \left( x \right).
Sketch the result of reflecting f \left( x \right) across the y-axis.
State the domain of the reflected function.
State the range of the reflected function.
When a function is reflected across the y-axis, does it affect the domain or range?
For each of the following functions f \left( x \right) and its corresponding graph:
f \left( x \right) = \left(x - 3\right)^{2}
f \left( x \right) = \dfrac{1}{3} x + 3
f \left( x \right) = \left| 2 x - 4\right|
f \left( x \right) = x^{3} - 2
For each of the following graphs of f \left( x \right) and g \left( x \right), write g \left( x \right) in terms of f \left( x \right) by considering the reflections that have occured on f \left( x \right) to get g \left( x \right):
Consider the function f \left( x \right) = x^{3} - 7 x^{2} + 10 x.
State the y-intercept of the function.
Determine the x-intercepts of the function.
Sketch the graph of:
f \left( x \right)
f \left( - x \right)
- f \left( x \right)
- f \left( - x \right)
The graph of a particular function f \left( x \right) has x-intercepts at \left( - 9 , 0\right) and \left(4, 0\right). State the \\ x-intercepts of the following graphs:
y = f \left( - x \right)
y = - f \left( x \right)
y = - f \left( - x \right)
A particular function f \left( x \right) is increasing on the interval \left(-\infty, 4\right) and decreasing on the interval \left(4, \infty\right). Describe the behaviour of the following functions on the interval \left(-\infty, \infty \right) :
Describe the overall effect on the graph of y = f \left( x \right) if is transformed to y = -f \left( -x \right).
Consider the graph of f \left( x \right) = x^{3} - 16 x :
Sketch the graph of - f \left( - x \right).
Comment on the graphs of f \left( x \right) and -f \left( -x \right).
Each of the following points A, lie on the curve y =f\left(x \right), State the coordinates of point A', the location of point A following the transformation y =-f\left(-x \right).
For each of the following functions f \left( x \right) and its corresponding graph:
f \left( x \right) = x^{2} - 3
f \left( x \right) = \left(x + 8\right)^{2}
f \left( x \right) = 2 x + 3
f \left( x \right) = \left| 2 x - 10\right|.
f \left( x \right) = x^{3} + 4
For each of the following graphs of f \left( x \right), sketch the graph of - f \left( - x \right):