<p>how do i find the domain and range of:</p>
<p>1/x +1</p>
<hr>
<p>1/x -3</p>
<p>read as onedivided by x plus 1 all divided by 1 divided by x minus 3</p>
<p>THANKS ALOt</p>
<p>please help all, I really need the answer soon</p>
<p>Domain</p>
<p>Since there aren't any functions in the given expression that could limit the domain (such as inverse sine), we go straight to finding the asymptote(s). Since division by 0 makes the expression undefined,</p>
<p>1/x - 3 != 0</p>
<p>1/x != 3</p>
<p>1 != 3x</p>
<p>1/3 != x</p>
<p>x != 1/3</p>
<p>x < 1/3, x > 1/3 is our domain.</p>
<p>Range</p>
<p>No one likes weird formulas, so let's simplify.</p>
<h2>1/x + 1</h2>
<p>1/x - 3</p>
<h2>1/x + x/x</h2>
<p>1/x - 3x/x</p>
<h2>(x+1)/x</h2>
<p>(-3x+1)/x</p>
<p>Now cancel the x's.</p>
<h2>(x+1)</h2>
<p>(-3x+1)</p>
<p>As x --> ∞, the expression becomes ∞/-3∞ so it approaches the value of -1/3.</p>
<p>As x --> -∞, the expression becomes -∞/3∞, which is also -1/3.</p>
<p>Since we still haven't found the other side of the range, we let x = 0, so we get 1/1 which makes 1.</p>
<p>So, the range is -1/3 < f(x) < 1.</p>
<p>Someone correct me in case I'm wrong, I have a slight tendancy to make small mistakes but I think that's right.</p>
<p>EDIT: I did in fact make one, corrected now.</p>
<p>thanks alot man!</p>
<p><sarcasm>Wow...</sarcasm></p>
<p>I so can't wait for high school now.</p>