02 Graphs And Transformations Flashcards
When does a cubic graph look like this?
When all 3 roots are the same (positive).
When does a cubic graph look like this?
When you have 3 different roots. (Positive)
When does a cubic graph look like this?
When you have 1 repeated root and one different root. (Positive)
When does a cubic graph look like this?
All 3 roots are the same (negative).
When does a cubic graph look like this?
3 different roots (negative).
When does a cubic graph look like this?
One repeated root and one different.
What is an a^x graph called?
An exponential function
What does an exponential graph look like (y = a^x)?
What type of graph is y = k/x (or y=k/x^2)?
A reciprocal graph
What type of graph is this?
Reciprocal (y=k/x)
Where are the asymptotes on a reciprocal graph?
X=0 and y=0
What is an asymptote?
A line which the graph approaches but never reaches.
What type of graph is this?
A reciprocal graph (y=k/x^2)
What type of graph is this?
A reciprocal graph (y=k/x^2)
How do you sketch a modulus graph?
Sketch the graph without the modulus, then reflect any sections of the graph below the x-axes.
What type of graph is this?
Modulus.
|-5| =
5
|5| =
5
Explain this translation.
Y =f(x) —> y = f(x) + a
Translation by the vector (0 a)
Explain this translation Y = f(x) —> y = f(x + a)
Translation by the vector (-a 0).
How is x awkward in translation?
Change the sign.
Explain this stretch.
Y = f(x) —> y = a f(x)
Stretch by a scale factor a in the y direction.
Explain the stretch.
Y = f(x) —> y = f(ax)
Stretch by a scale factor of 1/a in the x direction.
Why is x awkward in stretched graphs?
Use the reciprocal for the scale factor.
Explain the reflection
Y = f(x) —> y = -f(x)
Reflection in the x axis. (y = 0)
Explain the reflection
Y = f(x) —> y = f(-x)
Reflection in the y axis. (x = 0)
How do you reflect a graph vertically?
Multiply the function by -1 ‘outside the function’.
How do you reflect a graph horizontally?
Multiply the function by -1 ‘inside’ the function.
