Answer:
Linear, Quadratic, Radical, Absolute Value, Cubic, Cube Root
Step-by-step explanation:
To find:
Which functions have an intercept at (0, 0).
That means, when we put a value
in the
, value of
.
Let us discuss each <em>parent</em> function one by one:
1. Linear:
![y = x](https://tex.z-dn.net/?f=y%20%3D%20x)
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
2. Quadratic:
![y = x^2](https://tex.z-dn.net/?f=y%20%3D%20x%5E2)
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
3. Radical:
![y = \sqrt x](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%20x)
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
4. Absolute Value:
![y = |x|](https://tex.z-dn.net/?f=y%20%3D%20%7Cx%7C)
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
5. Rational:
![y = \dfrac{1}{x}](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B1%7D%7Bx%7D)
When we put ![x = 0\Rightarrow y \rightarrow \infty](https://tex.z-dn.net/?f=x%20%3D%200%5CRightarrow%20%20y%20%5Crightarrow%20%5Cinfty)
Therefore, it does not have intercept at (0, 0).
6. Exponential:
![y = b^x](https://tex.z-dn.net/?f=y%20%3D%20b%5Ex)
b is any base
When we put ![x = 0\Rightarrow y =1](https://tex.z-dn.net/?f=x%20%3D%200%5CRightarrow%20%20y%20%3D1)
Therefore, it does not have intercept at (0, 0).
7. Logarithmic:
![y = logx](https://tex.z-dn.net/?f=y%20%3D%20logx)
When we put
Not defined
Therefore, it does not have intercept at (0, 0).
8. Cubic:
![y = x^3](https://tex.z-dn.net/?f=y%20%3D%20x%5E3)
When we put ![x = 0\Rightarrow y =0](https://tex.z-dn.net/?f=x%20%3D%200%5CRightarrow%20%20y%20%3D0)
Therefore, it has intercept at (0, 0).
9. Cube Root:
![y = \sqrt[3]x](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5Dx)
When we put ![x = 0\Rightarrow y =0](https://tex.z-dn.net/?f=x%20%3D%200%5CRightarrow%20%20y%20%3D0)
Therefore, it has intercept at (0, 0).