Ingenuity Algebra 2, Quiz 4

What type of function is f(x) = x?

Linear

What does a linear function look like?

What type of function is f(x) = x²?

A quadratic function

What does a quadratic function look like?

What type of function is f(x) = x³?

A cubic function

What does a cubic function look like?

What type of function is f(x)=|x|?

An absolute value function

What does an absolute value function look like?

What type of function is f(x)= 1/x?

A rational function

What does a rational function look like?

What type of function is f(x) = e^x

An exponential function

What does an exponential function look like?

What type of function is f(x) = ln x

Logarithmic

What does a logarithmic function look like?

The one in purple

What type of function is f(x) = √x

Radical/square root function

What does a radical function look like?

When a transformation is added or subtracted by k, what does it look like?

f(x)= x ± k

How does the value of k transform the parent function?

Depending on ±, it either shifts all points/the function k units up or down. (x, y±k)

What does it mean when f (x) = (x±h)?

The function is horizontally shifted ∓ h units, respectively (x ± h, y)

What does it mean when f(x)=-(x)

The function is reflected over the x-axis (x, -y)

What does it mean when f(x) = (-x)

A reflection over the y-axis (-x, y)

What does it mean when f(x) = a(x), when |a| > 1

A vertical stretch: the function gets “skinnier” vertically: distance between x points shrink (imagine someone pulling on it vertically) (x, ay)

What does it mean for f(x) = a(x), when 0<a<1

A vertical compression: (It gets wider, distance between farthest horizontal points increases, imagine someone pushing down on it vertically)

What happens to a function when f(x) = bx when b>1

A horizontal compression: gets narrower, but imagine it more as it getting pushed toward the y-axis

What happens to a function when f(x) = (bx) when 0<b<1

A horizontal stretch: it gets wider, but imagine it as getting pulled on both sides, or away from the y axis.

What does it mean if a > 0 or a < 0 respectively for quadratics?

It will open up and have a minimum, or open down and have a maximum

What is the axis of symmetry for quadratics?

The vertical line that splits the quadratic into two symmetrical halves

The vertex is either the ________ or the _______ of a function

minimum, maximum

What is vertex form?

a(bx-h)²+k

Functions are congruent and similar if:

They have the same measurements and shape

Functions are similar and not congruent if:

They have the same shape, but different measurements (like by a constant scaling factor)

Functions are neither congruent or similar if

They are of different shapes and measurements.

What is true about even functions regarding the y axis?

They are symmetric with respect to the y axis

For even functions, it (x,y) is on the graph, then (_, _) must also be on the graph

(-x, y)

Odd functions are symmetric with respect to the ______

origin

For odd functions, if (x, y) is on the graph, then (_,_) must also be graphed

(-x, -y)

A function, algebraically, is even if:

f(x) = f(-x), meaning it stays the same after you’ve made all x’s into -x

A function, algebraically, is odd if:

-f (x)= f(-x). After multiplying everything by -1, the equation is the same as if you’d made multiplied all the x’s by -1.