Explain how you could graph each function by applying transformations. (a) y=log⁡(x−2)+7 (b) y=−3log⁡x (c) y=log⁡(−3x)−5

Question

Explain how you could graph each function by applying transformations. (a) y=log⁡(x−2)+7  (b) y=−3log⁡x  (c) y=log⁡(−3x)−5

wheezym · Accepted Answer

(a) Consider the given function y=log⁡(x−2)+7 To find the transformation of the graph of the given function First, draw the graph of the following function y=log⁡(x) Now, take horizontal shift right 2 units of the above So, y=log⁡(x−2) Again, take vertical shift up by 7 units of the above So, y=log⁡(x−2)+7 Hence, above are the required transformations. (b) Consider the given function y=−3log⁡x To find the transformation of the graph of the given function yyy===log⁡x−log⁡x (Reflection about the x−axis) −3log⁡x (Dilation with scale factor 3 −stretched vertical) Hence, the required transformations for the graph of the given function are reflection and dilation. (c) Consider the given function y=log⁡(−3x)−5 To find the transformation of the graph of the given function y=log⁡(x)y=log⁡(3x) (Dilation by scaling factor 3−stretched horizontal)y=log⁡(−3x) ( Reflection about the y−axis )y=log⁡(−3x)−5 (Vertical shift down 5 units ) Hence, the required transformations for the graph of the given function are dilation by scaling factor 3 units, reflection about the y-axis, and vertical shift down 5 units

Explain how you could graph each function by applying transformations.(a) y = log(x -2) + 7 (b) y = -3logx (c) y = log(-3x)-5

Answered question

Answer & Explanation

New Questions in High school geometry