![]() ![]() When the parent function is multiplied by a constant, the result is a vertical stretch or compression of the original graph. The new coordinates are found by subtracting 2 from the coordinates. This means we will shift the function down 2 units. Include the key points and asymptote on the graph. Sketch a graph of alongside its parent function. ĮXAMPLE 5 Graphing a Vertical Shift of the Parent Function The domain is, the range is, and the vertical asymptote is.Find new coordinates for the shifted functions by adding to the coordinate. Identify three key points from the parent function.shifts the parent function down units if.shifts the parent function up units if.To visualize vertical shifts, we can observe the general graph of the parent function alongside the shift up, and the shift down. When a constant is added to the parent function, the result is a vertical shift units in the direction of the sign on. Include the key points and asymptotes on the graph. The domain is, the range is, and the vertical asymptote is. The new coordinates are found by adding 2 to the coordinates. This means we will shift the function right 2 units.Ĭonsider the three key points from the parent function,, and. Sketch the horizontal shift alongside its parent function. ĮXAMPLE 4 Graphing a Horizontal Shift of the Parent Function The Domain is, the range is, and the vertical asymptote is.Find new coordinates for the shifted functions by subtracting from the coordinate. ![]() Given a logarithmic function with the form, graph the translation. shifts the parent function right units if.shifts the parent function left units if.To visualize horizontal shifts, we can observe the general graph of the parent function and for alongside the shift left,, and the shift right. When a constant is added to the input of the parent function, the result is a horizontal shift units in the opposite direction of the sign on. We can shift, stretch, compress, and reflect the parent function without loss of shape. As we mentioned in the beginning of the section, transformations of logarithmic graphs behave similarly to those of other parent functions.
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