%3D The transformation of a function f(x) into a function g(z) is given by g() = Af(Bx + H) + K. where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(z) into g(z) where the transformation is g(x) = f(x- 1) +3 %3D The function f(x) is shown below in red. Graph the transformed function g(a) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Transform the function by applying the constants in this order: H, B, A, K.) 4- 3- 2 -6 -5 -4 -3 -2 -1 -1 2 4. 5 -2 -3 -4- -5- -6- Clear All Draw: Dot Line Segment
Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
Given function is .
Comparing the function with , we obtain the following.
.
Vertical scaling: vertically scales the graph in y-axis (k>1 stretches the graph, 0<k<1 shrinks the graph vertically).
Horizontal scaling: Horizontally scales the graph in x-axis (k>1 shrinks the graph, 0<k<1 stretches the graph).
As there is no vertical scaling from the definition.
And as B=1 there is no horizontal scaling from the definition.
Horizontal shift: Shifts the function horizontally , if H>0 the function shifts right sided of x-axis, H<0 the function shifts left of x-axis.
Vertical shift: Shifts the function vertically , if k>0 the function shifts above y-axis, k<0 the function shifts below y-axis.
As H=-1 horizontally shifts the function. That is function is shifted to left side of x-axis.
K=3 vertically shifts the function. That is function is shifted above y- axis .
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