exam 3 Flashcards
Section 11.1
Define a function.
For every input there is exactly one output.
Section 11.1
The set of input values is called the (____) of the function.
domain
Section 11.1
The set of output values is called the (____) of the function.
range
Section 11.1
If no input (x) has more than one output (y), then it is…
a function
Section 11.1
If a vertical line can be drawn that (____) a graph at more than one point, the graph does not represent a function.
intersects
Section 11.1
What is the first step to solving this?
f(x) = 3x + 4, f(-3)
Replace “x” with “-3.”
Section 11.2
What is the slope formula of a linear function?
f(x) = mx + b
Section 11.2
When there is no identified y-intercept, it is…
the point (0, 0)
Section 11.2
What is the formula to find the slope of a function?
m = y2 - y1 / x2 - x1
When there are two points given of a graph, plug them in.
Section 11.2
What is the slope of this linear function?
f(x) = 2
There is no slope. It exists as “0x”.
11.3
What is the standard formula of a U-Shaped parabola?
f(x) = a(x - h)SQ + k
Section 11.3
What is the vertex in coordinates form?
(h, k)
Section 11.3
Recall the parent graph of a parabola.
f(x) = x(SQ)
Right one, up one, right two, up four…
Section 11.3
Explain the translation value of “h” in “(x - h) + k”
The translation of “h” is always the opposite of its assigned value.
Section 11.3
When graphing translations of “f(x) = (x - h)(SQ) + k”, how do you determine the shifts?
k = vertical shift/translation
h = horizontal shift/translation
Section 11.3
What is the rotation, horizontal shift, and vertical shift of the given function?
f(x) = (x + 13)(SQ) - 7
No reflection. Left 13. Shift down 7.
There is no reflection because the function is positive.
11.3
What is the rotation, horizontal shift, and vertical shift of the given function?
f(x) = - (x - 4)(SQ) + 30
Reflection. Shift right 4. Shift up 30.
Remember the horizontal shift is opposite of its value.
11.3
The smallest possible output of a function is called the…
minimum value.
11.3
The greatest possible output of a function is called the…
maximum value.
11.3
The maximum/minimum value is only the…
A. input (x)
B. output (y)
C. both (x, y)
B. output (y)
11.3
You can find the minimum/maximum output by finding the…
Vertex.
11.3
What is the formula for slope of a secant?
f(x+h) - f(x) / h
11.3
How do you solve
f(x) = x(SQ) + 3x + 317
when you simplify the difference quotient
f(x+h) - f(x) / h?
Plug in (x+h) into the “x” placements of the f(x) equation given and then subtract the original f(x) equation from that, then divide it over h.
11.4
When you define the range, think of it like an elevator moving …
from the bottom to the top.
11.4
When defining the domain, think of it like reading a book…
from left to right.
11.4
What is the parent graph of an absolute value function?
f(x) = | x |
left one, up one, left two, up two…
11.4
What is the vertex formula for an absolute value function?
f(x) = a|x - h| + k
11.4
If “a” is negative, then…
IF “a” in “ a|x - h| + k”…
it faces downwards.
11.4
If “a” is positive…
IF “a” in “ a|x - h| + k”…
it faces upwards.
11.4
What is the parent graph of a square root function?
f(x) = (SQRT of)x
right one, up one, right four, up two, right nine, up three…
11.4
What is the standard (vertex) form of a square root function?
f(x) = (SQRT of)(x - h) + k
11.4
Explain the difference to our square root function graph when a negative is outside the square root and when a negative is inside the square root.
When a negative is outside the square root, it reflects downwards. It flips vertically.
When a negative is on the inside of the square root, it reflects horizontally.
11.4
What is the parent graph of a cubic function?
f(x) = x(CUBED)
11.4
A cubic function doesn’t have a vertex, it has a…
point of inflection.
11.4
What is the standard (vertex) form of a cubic equation?
f(x) = (x - h)(CUBED) + k
11.5
Define the sum function.
For any two functions f(x) and g(x),
(f + g)(x) = f(x) + g(x).
11.5
Define the difference function.
Opposite of addition.
For any two functions f(x) and g(x),
(f - g)(x) = f(x) - g(x).
11.5
Define the production function.
For any two functions f(x) and g(x),
(f x g)(x) = f(x) x g(x).
11.5
Define the quotient function.
For any two functions f(x) and g(x),
(f / g)(x) = f(x) / g(x).
g(x) cannot equal 0.
11.5
Define the composite function.
For any two functions f(x) and g(x),
(f o g)(x) = f(g(x)).
Works vise verse for g(f(x)).
The symbol “o” is used to denote the composition of two functions.
11.6
A function sends one value in the () to only one value in the ().
domain.
range.
11.6
A one-to-one function that has every element in range corresponding to at most () in the domain.
one element
11.6
In other words for each f(x) or () there is only one input () that will yield f(x).
output.
“x”
11.6
Is this a one-to-one function?
{(-7,-5)(-5,-2)(-2,4)(3,3)(6,-7)}
This is a function.
It is a one-to-one function.
11.6
What is the horizontal line test?
If a horiztonal line can intersect a graph at more than one point, the function is not one-to-one.
11.6
Inverse functions (a) what a functions does. For example the point (3,7). The (b) gets sent to a (c). The inverse of f(x) will send a (d) to a (e).
a. undoes
b. 3
c. 7
d. 7
e. 3
11.6
Two one-to-one functions f(x) and g(x) are inverse functions if …
(f o g)(x) = x
and
(g o f)(x) = x
11.6
What are the five steps to finding the inverse of a function?
- Determine whether f(x) is one-to-one.
- Replace f(x) with y.
- Interchange x and y.
- Solve the resulting equation for y.
- Replace y with F-1(x).
11.6
A function and its inverse are always…
(when graphed)
symmetrical
