Pure- Graphs and transformations (4) Flashcards
What is the form of a cubic equation?
f(x)=ax^3 + bx^2 + cx + d
where a,b,c,d are real numbers and a isn’t 0
What happens if p is the root of f(x)?
y=f(x) touches or crosses the x-axis at (p,0)
What is the form a quartic equation?
f(x)=ax^4 + bx^3 +cx^2 + dx + e
What are the asymptotes of y=k/x and y=k/x^2 where k is a real constant?
x=0
y=0
What is an asymptote?
A line which the graph approaches but never reaches.
What are the x-coordinates to the intersections of y=f(x) and y=g(x)?
The solutions to f(x)=g(x)
What transformation does y=f(x)+a correspond to ?
A translation of y=f(x) by a units vertically
What transformation does y=f(x+10) correspond to?
A translation of y=f(x) by -a units horizontally
What does the transformation y=af(x) correspond to?
A vertical stretch of y=f(x) by scale factor a
What does the transformation y=f(ax) correspond to?
A horizontal stretch of y=f(x) by scale factor 1/a
What does the transformation y=-f(x) correspond to?
A reflection of y=f(x) in the x-axis
What does the transformation y=f(-x) correspond to?
A reflection of y=f(x) in the y-axis