# ⚛ Library of functions ⚛

# f(x) = x^2

It is the square root function, also known as a parabola!

Its domain is all reals.

The range for it is 0 to positive numbers of infinity, including 0.

The zero for this graph is x=0.

It has y-axis symmetry.

Since it has y-axis symmetry, it is an even function.

This function is not periodic.

This function is not a one-to-one function.

An example of the function:

# ☼ f(x) = x^3 ☼

The domain is all reals.

The range is all reals except (0, ∞), only with positive integers for infinity.

The x-intercept is when x=0.

It has origin symmetry.

Since it has origin symmetry, it is an odd function.

It is not a periodic function.

It is a one-to-one function.

An example of the function:

# ♛ f(x) = |x| ♛

# ▲ f(x) = sin x ▲

This graph could be nicknamed the "hills and valley" graph.

Its domain is all reals.

It ranges from [-1,1].

Its zeros are integral multiples of π.

It has origin symmetry, therefore it is an odd function.

Yes, the function is periodic.

No, it is not a one-to-one function.

Here's an example of the graph:

# ツ f(x) = cos x ツ

This function is also a hills and valley type of function!

Its domain is all reals.

Alike from the sin graph, its range is also [-1,1].

Its zeros are odd multiples of π/2.

It has y axis symmetry, therefore it is an even function.

Yes, it is a periodic function.

No, it is not a one-to-one function.

This is an example of the graph:

This graph is in the shape of a wide v.

The domain is all reals.

The range is (0,

The x-intercept is when x=0.

This function has y-symmetry.

Since it has y-symmetry, it is an even function.

No, it is not a periodic function.

No, it is not one-to-one.

Here is an example of the function:

# ♚ f(x) = tan x ♚

Its domain is all reals except for odd multiples of π/2.

Its range is all reals.

Its x-intercepts are multiples of π.

It has origin symmetry, so it is an odd function.

Yes, it is one to one.

No, it is not a one-to-one function.

Here is the graph:

# ❅ f(x) = sec x ❅

Similar to the tan graph, its domain is all reals but odd multiples of π/2.

Its range is [1, ∞)∪(-∞,-1].

It has no x-intercepts.

It has y-axis symmetry, so it is an even function.

Yes, the function is periodic.

No, it is not one-to-one.

Here is the graph:

# ⚛ f(x) = 2^x ⚛

Its domain is all reals.

It ranges from (0,∞) as long as y > o.

It has no x-intercepts.

It has no symmetry, so it is neither an even or odd function.

No, it is not a periodic function.

Yes, it a one-to-one function.

Here is an example of the graph:

# ☮ f(x) = log2x ☮

The domain for this function is (0,∞).

The range is all reals.

It intercepts x at x = 1.

It has no symmetry, therefore it is neither an odd or even function.

No, it is not a periodic function.

Yes, it is a one-to-one function.

Here is a photo of the graph:

# f(x) = 1/x

Its domain is (-∞,1)∪(1,-∞).

Its range is all reals.

It has no x-intercepts.

It has origin symmetry, therefore it is an odd function.

No, it is not a periodic function.

Yes, it is a one to one function.

Here is an example of the function:

# ✿ f(x) = sqrt(x) ✿

The domain for this function is [0,∞).

Its range is [0,∞).

The x-intercept for this graph is when x=0.

There is no symmetry for this specific graph, so it has neither an odd or even function.

No, it is not a periodic function.

Yes, it is actually a one-to-one function.

Here is an example of the graph:

# f(x) = sqrt of a^2-x^2

Its domain is [-a,a].

The range for this graph is [0,a].

It has x-intercepts when x=a,-a.

It has y-axis symmetry so therefore it is an even function.

It is neither a periodic or one-to-one function.

Here is an example of the graph: