Select ALL the functions whose graphs include the point (16,4) y=2x y=x-12 y=x+12 y=1/4x y=x^ast x

To determine which functions include the point $$(16,4)$$ , we need to substitute the x-coordinate (16) into each function and see if the resulting y-value is 4.

1. $$y=2x$$
Substituting x=16, we get $$y=2(16)=32$$ , which is not equal to 4. So, this function does not include the point $$(16,4)$$ .

2. $$y=x-12$$
Substituting x=16, we get $$y=16-12=4$$ , which is equal to 4. So, this function includes the point $$(16,4)$$ .

3. $$y=x+12$$
Substituting x=16, we get $$y=16+12=28$$ , which is not equal to 4. So, this function does not include the point $$(16,4)$$ .

4. $$y=\frac{1}{4}x$$
Substituting x=16, we get $$y=\frac{1}{4}(16)=4$$ , which is equal to 4. So, this function includes the point $$(16,4)$$ .

5. $$y=x^{\ast }x$$
Substituting x=16, we get $$y=16^{\ast }16=256$$ , which is not equal to 4. So, this function does not include the point $$(16,4)$$ .

Therefore, the functions whose graphs include the point $$(16,4)$$ are:
- $$y=x-12$$
- $$y=\frac{1}{4}x$$