Set 1 (base) Flashcards
State the Quadratic formula
State the distance formula
d=
show f(x) when translated h units in the positive direction of the horizontal axis.
f(x-h)
State the rule for the function
log(a)+log(b)
log(ab)
quick sketch
value of discriminant when 2 solutions
> 0
greater than 0
If the gradient of 2 equations is the same and the y-int is the same how many solutions do they have?
infinite
State the rule for the function
state the discriminant
value of discriminant when 1 solution
= 0
state the expression for the axis of symmetry
State the rule for the function
value of discriminant when no solution
< 0
less than 0
show f(x) when reflected in the vertical axis
f(-x)
State the rule for the function
show f(x) when dilated by a factor of a from the horizontal axis
af(x)
If the gradient of 2 equations is different, how many solutions do they have?
1
State the rule for the function
log(a^b)
blog(a)
log(1)
0
How does the domain of the inverse relate to the original function?
It is equivalent to the range.
show f(x) when dilated by a factor of a from the vertical axis
f(x/a)
show f(x) when translated k units in the positive direction of the vertical axis.
f(x)+k
State the equation of a linear line.
quick sketch
log(a)-log(b)
If the gradient of 2 equations is the same but different y-int how many solutions do they have?
0
show f(x) when reflected in the horizontal axis
-f(x)
State the rule for the function
state the midpoint coordinate rule
State the rule for the function
Quick sketch of base graph for y=e^x
(this is the same as for any exponential graph in the form y=a^x, where a>1)
Quick sketch of base graph for y=ln(x)
Note: this is the same as for any graph of y=log(x) for ANY base (eg, log2(x))
Quick sketch of y=x^3
Note, same rough shape for the graph of any function y=x^(positive odd integer >1)
eg: x^5, x^7, x^9…
Quick sketch of y=x^4
Note, same rough shape for the graph of any function y=x^(positive even integer >1)
eg: x^2, x^4, x^6…
Note, same rough shape for the graph of any function y=x^(1/even positive integer)
eg: x^1/2, x^1/4, x^1/6…
Note, same rough shape for the graph of any function y=x^(1/even odd integer >1)
eg: x^(1/3), x^(1/5), x^(1/7)…
Note, same ROUGH shape for the graph of any function y=1/x^(odd integer >1)
eg: 1/x^(3), 1/x^(5), 1/x^(7)…
Note, same ROUGH shape for the graph of any function y=1/x^(even integer >1)
eg: 1/x^2, 1/x^4, 1/x^6…
Formula for completing the square
