Graphing Some Important Functions (3.12.1)

Question 1

• This lecture presents some basic equations with their graphs. Becoming familiar with linear, quadratic, cubic, radical and
absolute value equations and their graphs is important.

Answer 1

• This lecture presents some basic equations with their graphs. Becoming familiar with linear, quadratic, cubic, radical and
absolute value equations and their graphs is important.

Question 2

Consider the equation f (x) = c.
Every point on the line matches some x with the same value
for y (or c in this case). The line is not moving at all on the
vertical scale; therefore, it is horizontal.
Every point changes x- and y-values exactly the same. So
you get a line that divides the matching-signs quadrants
exactly in half.
The function of f (x) = x is the linear function.
Parabolas are guaranteed symmetry by the x
2
term which
neutralizes the signs of the values for x.
The function f (x) = x
2
is the quadratic parent function.
This curve will rise three times faster than it moves sideways
thanks to the impact of the x
3
term.
The funtion f (x) = x
3
is the cubic parent function.
Remember: The value under the radical must be greater
than or equal to zero so that a real number root can exist.
The function f (x) = is the radical parent function.
Note that a positive whole number can have two square roots:
a positive root and a negative root. However, when the radical
function is evaluated for any positive number, the only
solution is the positive square root, or principal square root,
as is generally the case in common usage unless otherwise
stated. Therefore, an equation containing a radical is a
function.

Answer 2

Consider the equation f (x) = c.
Every point on the line matches some x with the same value
for y (or c in this case). The line is not moving at all on the
vertical scale; therefore, it is horizontal.
Every point changes x- and y-values exactly the same. So
you get a line that divides the matching-signs quadrants
exactly in half.
The function of f (x) = x is the linear function.
Parabolas are guaranteed symmetry by the x
2
term which
neutralizes the signs of the values for x.
The function f (x) = x
2
is the quadratic parent function.
This curve will rise three times faster than it moves sideways
thanks to the impact of the x
3
term.
The funtion f (x) = x
3
is the cubic parent function.
Remember: The value under the radical must be greater
than or equal to zero so that a real number root can exist.
The function f (x) = is the radical parent function.
Note that a positive whole number can have two square roots:
a positive root and a negative root. However, when the radical
function is evaluated for any positive number, the only
solution is the positive square root, or principal square root,
as is generally the case in common usage unless otherwise
stated. Therefore, an equation containing a radical is a
function.

Question 3

Remember: Absolute value is always positive and graphed
along the positive axis regardless of the expression within its
notation.
The function f (x) = is the absolute value parent function.

Answer 3

Remember: Absolute value is always positive and graphed
along the positive axis regardless of the expression within its
notation.
The function f (x) = is the absolute value parent function.