Vertical stretch/ shrink

Graph is taller or shorter, controlled by coefficients outside parentheses, when coefficient is greater that 1 its vertical stretch. When between 0 and 1 its vertical shrink.

Moves graphs up or down, controls addition or subtraction outside parentheses

What are the transformations of this equation? 1/3(-2/5x+1)^2-9

X^2 function +1 = left 1, 2/5 coefficient inside parentheses= Horizontal stretch by 5/2, 1/3 coefficient outside parentheses = vertical shrink by 1/3. Negative coefficient inside = reflect over y-axis, -9 outside = down 9

Horizontal shifts left 3, reflect over x-axis, vertical shifts, down 6

Horizontal shift, right 4 reflected over y-axis vertical stretch 3, vertical shift down.

for functions define in pieces. To find f(x) locate the piece that applies to your given function. 1. Boundaries of end points 2. Graph each expression - use xy tables - use x values in the domains -use ends/boundries

t-5t, t≤-10 f(x)= { t+19, -10<t<-2 t^3/t+9, t≥-2 What is the value of f(-10)?

150 f(-10)=(-10)^2-5(-10) 100+150 =150

Find the specified value for the following functions? 4x-3, for x<2 f(x)= { 5,for 2≤x≤4 2x, for x>4 Find f(-3), f(2), f(7)

f(-3)= -15 (-3,(5) f(2)= 5 4(2)-3=5 f(7)=14 2(7)=14

How do you convert an equation to standard form?

To convert an equation to standard form, rearrange it so that it is in the form Ax + By = C, where A, B, and C are integers, and A should be non-negative.

To find the vertex of a quadratic equation in the form ax^2 + bx + c, use the formula: vertex = (-b/2a, f(-b/2a)).

How can we tell if a function has an inverse?

x axis: f(x)=-f(x) y axis: f(x)=f(-x) Origin: f(x)=-f(-x)

How can we tell if a function has an inverse?

One to one (passes vertical and horizontal line test. No recreating x or y values)

How can we identify where a graph is decreasing, increasing, or constant? How can we identify local maximums and minimums?

How to tell where a graph is increasing, decreasing, or constant: A graph is increasing where it goes up as you move from left to right. It's decreasing where it goes down as you move from left to right. It's constant where it stays flat (a straight, horizontal line). How to find local maximums and minimums: A local maximum is a high point (a hilltop) on the graph. A local minimum is a low point (a valley) on the graph. These are places where the graph changes direction — from going up to down (max), or down to up (min).

What is the difference between a function and a relation

Function has no repeating x values

How can we identify if a value is a zero of a function?

Plug the value into the function. If you get 0 as the output (y-value), then the value is a zero .

The points (2,0), (4,-4) and (6,2) are on f(x). Find the transformed points on the following function: 𝑔(𝑥) = −3𝑓(2𝑥 − 4) − 1

(2,0) = (3,-1) (4,-4) = (4,11) (6,2) = (5,-7)

Identify the transformation: y=-(x-4)^2+2

Reflect over x-axis, shift right 4, shift up 2

Horizontal Transformations in Functions Flashcards

Student preview

48 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What controls the horizontal shift in a function?

Back

Add/subtract in parentheses.

2.

FLASHCARD QUESTION

Front

Which direction does a function shift with addition in parentheses? Left or right

Back

Left

3.

FLASHCARD QUESTION

Front

Which direction does a function shift with subtraction in parentheses? Right or left

Back

Right

4.

FLASHCARD QUESTION

Front

What is horizontal stretch?

Back

A transformation that stretches the graph of a function horizontally.

5.

FLASHCARD QUESTION

Front

What Horizontal transformation is represented by (2x)^2?

Back

Horizontal Shrink by 1/2

6.

FLASHCARD QUESTION

Front

How does a horizontal stretch or shrink affect a graph?

Back

The graph either widens or narrows. Elements like radicands, denominators, and absolute values are considered as if inside parentheses. A coefficient greater than 1 results in a shrink, while a coefficient between 0 and 1 results in a stretch.

7.

FLASHCARD QUESTION

Front

what horizontal transformation does this show?

√2/5x

Back

Stretch by 5/2

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