Answer:
A, C, D, E, F
Step-by-step explanation:
A parent cubic function goes through the origin because its parent function y=x^3 means you can plug in (0,0) as 0=0^3.
A reciprocal function does not go through the origin because its parent function y=1/x does not allow (0,0) to be plugged in as you cannot divide by 0.
A parent quadratic function goes through the origin because its parent function y=x^2 means you can plug in (0,0) as 0=0^2
A parent absolute value function goes through the origin because its parent function y=|x| means you can plug in (0,0) as 0=|0|
A parent linear function goes through the origin because its parent function y=x means you can plug in (0,0) as 0=0
A parent cube root function goes through the origin because its parent function y=cbrt(x) means you can plug in (0,0) as 0=cbrt(0)
The parent function is the base of a function family.
The functions that go through the origin are:
The origin is represented as: (0,0)
A. Cubic function
A cubic function is represented as:
[tex]y = x^3[/tex]
Substitute 0 for x
[tex]y = 0^3[/tex]
[tex]y = 0[/tex]
This means that it passes through origin at (0,0)
B. Reciprocal function
A reciprocal function is represented as:
[tex]y =\frac 1x[/tex]
Substitute 0 for x
[tex]y =\frac 10[/tex]
[tex]y = und efine d[/tex]
This means that it does not pass through origin at (0,0)
C. Quadratic function
A quadratic function is represented as:
[tex]y = ax^2[/tex]
Substitute 0 for x
[tex]y = a \times 0^2[/tex]
[tex]y = 0[/tex]
This means that it passes through origin at (0,0)
D. Absolute function
An absolute function is represented as:
[tex]y = |x|[/tex]
Substitute 0 for x
[tex]y = |0|[/tex]
[tex]y = 0[/tex]
This means that it passes through origin at (0,0)
E. Linear function
A linear function is represented as:
[tex]y = mx[/tex]
Substitute 0 for x
[tex]y = m \times 0[/tex]
[tex]y = 0[/tex]
This means that it passes through origin at (0,0)
F. Cube root function
A cube root function is represented as:
[tex]y = \sqrt[3]{x}[/tex]
Substitute 0 for x
[tex]y = \sqrt[3]{0}[/tex]
[tex]y = 0[/tex]
This means that it passes through origin at (0,0)
Hence, the base functions of all the function except the reciprocal function pass through the origin
Read more about parent functions at:
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