Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.A. 5B. [tex]\frac{1}{5}[/tex]C. -[tex]\frac{1}{5}[/tex]D. -5

Accepted Solution

Answer:Option A k=5Step-by-step explanation:step 1Find the equation of f(x)we have the points(-10,-6) and (0,4)Find the slope m[tex]m=(4+6)/(0+10)=1[/tex]The function in slope intercept form is equal to[tex]f(x)=mx+b[/tex]we have[tex]m=1[/tex][tex]b=4[/tex] -----> the point (0,4) is the y-interceptsubstitute[tex]f(x)=x+4[/tex]step 2Find the equation of g(x)we have the points(-2,-6) and (0,4)Find the slope m[tex]m=(4+6)/(0+2)=5[/tex]The function in slope intercept form is equal to[tex]g(x)=mx+b[/tex]we have[tex]m=5[/tex][tex]b=4[/tex] -----> the point (0,4) is the y-interceptsubstitute[tex]g(x)=5x+4[/tex]step 3Find the value of kwe have[tex]f(x)=x+4[/tex][tex]g(x)=5x+4[/tex] -----> equation A[tex]g(x)=f(kx)[/tex] -----> equation B[tex]f(kx)=kx+4[/tex] ----> equation Csubstitute equation A and equation C in equation B and solve for k[tex]kx+4=5x+4[/tex] [tex]kx-5x=0\\kx=5x\\k=5[/tex]