Evaluating Functions
Composing Functions
Transforming Graphs
Transforming Equations
Inverses of Functions
100
This is g(9) when g(a) = 3/a
What is
g(9) = 1/3?
100
f(x) = x + 1
g(x) = 3x
This is f(g(2))
What is f(g(2)) = 7?
100
The set of transformations that has happened to f(x) = |x| to create this graph.
f(x) has been reflected over the x-axis then translated 3 units up
100
f(x) = 2x - 3 reflected over the x-axis
-f(x) = -2x + 3
100
This function is the inverse of h(x) = x + 1
What is
h^-1(x) = x - 1?
200
This is m(4) when m(x) = \frac{x+2}{9}
What is
\frac{2}{3} = 0.bar6
?
200
f(x) = x + 1
g(x) = 3x
This is g(f(2))
What is g(f(2)) = 9?
200
The set of transformations that happened to create this graph from the parent function f(x) = x
What is: reflected over the y-axis and vertically stretched by a factor of 1/2?
200
f(x) = 2x - 3 reflected over the y-axis
f(-x) = -2x - 3
200
This function is the inverse of p(t) = \frac{t}{21}
What is
p^-1(t) = 21t
?
300
In this graph of f(x), this is f(3)
f(3) = -3
300
a(x) = -\frac{2x+1}{4}
b(x) = 4x^2
This is b(a(x))
b(a(x)) = 4[\frac{2x+1}{4}]^2
300
The purple graph is |x|. What is the equation of the orange graph?
-|3x|
300
g(x) = 5x + 1 translated 3 units left
g(x+3) = 5(x+3) + 1 = 5x + 16
300
The inverse of the function r(s) = 2s + 5:
What is
r^-1(s) = \frac{s-5}{2}
?
400
Let f(x) = 4x^2-3 .
Let g(x) = \frac{x-5}{5}
What is f(g(15))?
f(g(15)) = 13
400
DOUBLE JEOPARDY
m(x) = |-x - 2|
n(x) = 1/4 x + 3
p(x) = 3 - sqrt(x)
This is p(n(m(2)))
What is p(n(m(2))) = 1?
400
This quadratic graph has been only TRANSLATED from f(x) = x2. What translations have taken place?
f(x) = x2 has been translated 2 units right and 4 units down.
g(x) = (x-2)2 - 4
400
h(x) = 8|x - 3| translated 4 units down THEN reflected in the x-axis
Translated down: h(x) - 4 = 8|x - 3| - 4
Reflected in x-axis: -[h(x) - 4] = -(8|x-3| - 4) = 8|x - 3| + 4
400
The slope of the inverse of this function
What is 3?
500
This is p(-2) when
p(t) = abs(t^3-3)t
p(-2) = abs((-2)^3-3)(-2)
p(-2) = abs(-6-3)(-2)
p(-2) = abs(-9)(-2)
p(-2) = 9(-2)
p(-2) = -18
500
purple(orange(-1))
purple(orange(-1)) = -4
500
What transformations turn the GREEN function into the BLACK function?
horizontally stretch by 1/4
translate up 1
500
h(x) = 8|x - 3| reflected in the x-axis THEN translated 4 units down
reflected in the x-axis: -h(x) = -8|x - 3|
translated 4 units down: -h(x) - 4 = -8|x - 3| - 4
500
DOUBLE JEOPARDY
Find the inverse of f(x) = \frac{x}{x-19}
\frac{19x}{x-1}