What is a simple way for me to remember parent functions?I have been having some trouble remembering in Algebra 2.

An excellent way to remember a parent function is to
associate the function to it's graph. The visual aspect plays an important role in
helping someone to memorise something.

For instance, for
the constant function f(x)=a , the graph is a line parallel to x
axis.

If a = 3, the graph of the function f(x)=3 is the red
line, parallel to x axis, that intercepts y axis at
y=3.

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-7.5,7.5,-5,5,1,1,1,1,1,300,200,func,3,null,0,0,,,red,1,none"/>

For
a linear function, f(x) = ax + b, the graph is a line that is no longer parallel to x
axis.

For instance, if f(x) = x + 3, the graph is the red
line that intercepts x axis at the point (-3,0) and y axis at (0 , 3). type="image/svg+xml"
src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-7.5,7.5,-5,5,1,1,1,1,1,300,200,func,x+3,null,0,0,,,red,1,none"/>

If
the parent function is a quadratic, the graph will be a upward or downward
concave parabola, that will intercept the x axis in two distinct points, one point or no
point, depending on the nature of the roots
of quadratic.

For instance, a quadratic that has two
roots,it will look like:

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-7.5,7.5,-5,5,1,1,1,1,1,300,200,func,x^2-5x+6,null,0,0,,,red,1,none"/> upward
concave

or

type="image/svg+xml"
src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-7.5,7.5,-5,5,1,1,1,1,1,300,200,func,-x^2+5x-6,null,0,0,,,orange,1,none"/>downward
concave

The parabola that has two equal roots it will look
like:

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-7.5,7.5,-5,5,1,1,1,1,1,300,200,func,(x-1)^2,null,0,0,,,red,1,none"/>

You
notice that the values of the equal roots gives the location of the vertex, that is
tangent to x axis. Of course, there is a downward concave version,
also.

You can also keep in mind that the logarithmic
function is the inverse function of exponential function and the graph of logarithmic
function can be found if we'll mirror the graph of exponential function, with respect to
the 1st bisectrix.

Therefore, keep in mind
that the visual aspect helps you to remember much more easier the family of parent
functions.