Function $$g$$ is a horizontally scaled version of function $$f$$. The functions are graphed where $$f$$ is solid and $$g$$ is dashed. What is the equation of $$g$$ in terms of $$f$$ ?

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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>Function $$g$$ is a horizontally scaled version of function $$f$$. The functions are graphed where $$f$$ is solid and $$g$$ is dashed. What is the equation of $$g$$ in terms of $$f$$ ?

![](http://admin.getprephub.com/media/editor/te21_20230116210826580039.png)</textarea>Function <math><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math>g is a horizontally scaled version of function <math><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math>f. The functions are graphed where <math><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math>f is solid and <math><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math>g is dashed. What is the equation of <math><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math>g in terms of <math><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math>f ?
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Here $$g$$ is squashed version of $$f$$.Therefore $$g(x)=f(k x)$$

$$f$$ passes through $$(4,3) g$$ passes through $$(2,3)$$.

Comparing,$$\frac{4}{k}=2$$

$$ k=\frac{4}{2}=2 $$ 

Therefore, the equation og $$g$$ in terms of $$f$$ is$$g(x)=f(2 x) $$ </textarea>Here <math><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math>g is squashed version of <math><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math>f.Therefore <math><semantics><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mi>k</mi><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">g(x)=f(k x)</annotation></semantics></math>g(x)=f(kx)
<math><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math>f passes through <math><semantics><mrow><mo>(</mo><mn>4</mn><mo separator="true">,</mo><mn>3</mn><mo>)</mo><mi>g</mi></mrow><annotation encoding="application/x-tex">(4,3) g</annotation></semantics></math>(4,3)g passes through <math><semantics><mrow><mo>(</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(2,3)</annotation></semantics></math>(2,3).
Comparing,<math><semantics><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mi>k</mi></mrow></mfrac><mo>=</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">\frac{4}{k}=2</annotation></semantics></math>​k​​4​​=2
<math><semantics><mrow><mi>k</mi><mo>=</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mn>2</mn></mrow><annotation encoding="application/x-tex"> k=\frac{4}{2}=2 </annotation></semantics></math>k=​2​​4​​=2 
Therefore, the equation og <math><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math>g in terms of <math><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math>f is<math><semantics><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">g(x)=f(2 x) </annotation></semantics></math>g(x)=f(2x) 
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