Graph the function y=f(x)=x3−5. match each of its translations with its respective graph. tiles y=f(x/5) y=f(x−5) y=f(x)+10 y=f(5x−2)

Answer with explanation:

The given function is

 y=f(x)=x³ -5

Function with Translation

The graph of function shown below.

Step-by-step explanation:

The given function is

The graph of this function is the graph of parent function after shifting 5 units down.

The translation is defined as

               .... (2)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph stretch horizontally by factor 1/k and if k>1, then the graph compressed horizontally by factor 1/k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The given functions are :

1.

Here, k=1/5. So the graph of f(x) stretch horizontally by factor 5.

2.

Here, a=-5, So, the graph of f(x) shifts 5 units right.

3.

Here, b=10, So, the graph of f(x) shifts 10 units up.

4.

Here, k=5 and a=-2, So, the graph of f(x) compressed horizontally by factor 1/5 and shifts 2 units right.

The graph of function shown below.

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step-by-step explanation: