 The function $${f}$$ is defined for all real numbers. What is a reasonable estimate for $$\lim _{x \to-5} f(x)$$ ?

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<div id="displayOption0" class="markdown-body editormd-html-preview"><textarea>Limit does not exceed</textarea>Limit does not exceed
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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea> The function $${f}$$ is defined for all real numbers. What is a reasonable estimate for $$\lim _{x \to-5} f(x)$$ ?

![](http://admin.getprephub.com/media/editor/l8_20220921224039707853.png)</textarea> The function <math><semantics><mrow><mrow><mi>f</mi></mrow></mrow><annotation encoding="application/x-tex">{f}</annotation></semantics></math>f is defined for all real numbers. What is a reasonable estimate for <math><semantics><mrow><msub><mi>lim</mi><mrow><mi>x</mi><mo>→</mo><mo>−</mo><mn>5</mn></mrow></msub><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">\lim _{x \to-5} f(x)</annotation></semantics></math>lim​x→−5​​f(x) ?
<img src="http://admin.getprephub.com/media/editor/l8_20220921224039707853.png" alt="">
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Here from the graph,
 $$f(-5)=1$$

when $$x \to-5^{+} ,f(x)$$ approaches $$1$$ ,

and when $$x \to -5^{-} f(x)$$ approaches $$-4$$.

$$\therefore$$ linit does not exist.

</textarea>Here from the graph, <math><semantics><mrow><mi>f</mi><mo>(</mo><mo>−</mo><mn>5</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">f(-5)=1</annotation></semantics></math>f(−5)=1
when <math><semantics><mrow><mi>x</mi><mo>→</mo><mo>−</mo><msup><mn>5</mn><mrow><mo>+</mo></mrow></msup><mo separator="true">,</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">x \to-5^{+} ,f(x)</annotation></semantics></math>x→−5​+​​,f(x) approaches <math><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math>1 ,
and when <math><semantics><mrow><mi>x</mi><mo>→</mo><mo>−</mo><msup><mn>5</mn><mrow><mo>−</mo></mrow></msup><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">x \to -5^{-} f(x)</annotation></semantics></math>x→−5​−​​f(x) approaches <math><semantics><mrow><mo>−</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">-4</annotation></semantics></math>−4.
<math><semantics><mrow><mo>∴</mo></mrow><annotation encoding="application/x-tex">\therefore</annotation></semantics></math>∴ linit does not exist.
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