## anonymous one year ago Help please with domain and range :) Picture attached.

1. anonymous

2. ybarrap

The term in the radical can not be negative and the denominator itself can no be zero. This implies that $$x-6 > 0\implies x>6$$. This gives the domain. Note that $$x=6$$ is not allowed, because that would make the denominator zero. Since the square root is always positive and all positive values close to 6 are allowed and as x gets closer to 6 the value of this function, let's call it y, approaches infinity, so $$y> 0$$ is the range. Note that $$y=0$$ is excluded because as x approaches infinity, y approaches zero but never reaches it. For both the domain and the range, infinity is not included at the endpoint. Domain: $$(6,\infty)$$ Range: $$(0,\infty )$$ https://www.wolframalpha.com/input/?i=plot+1%2Fsqrt%28x-6%29+%2C+6%3Cx%3Cinfinity

3. anonymous

thank you so much!