Mathematics
norakins
2016-09-22 15:48:39
Write the expression for the function whose graph is the graph of y = x^3 but shifted down 4 units and left 5 units. A. y = (x - 5)^3 - 4 B. y = (x + 5)^3 - 4 C. y = (x - 5)^3 + 4 D. y = (x - 4)^3 - 5
ANSWERS
ShizukoCleary
2016-09-22 17:24:17

1. Consider y=f(x) 2. let a and b be 2 positive numbers 3. then the graph of y=f(x)-a is the graph of y=f(x) shifted a units down 4. the graph of y=f(x+b) is y=f(x) shifted b units left                         y=f(x-b)  is y=f(x)  shifted b units right 5. y=f(x+b)-a is the graph of y=f(x) shifted a units down and b units left 6. So [latex]y=x^{3} [/latex] shifted 4 units down and 5 units left is the graph of                        [latex]y=(x+5)^{3}-4 [/latex] 7. To check: consider [latex]y=x^{3}[/latex] at x=3. We have the point (3, 27)      Shift this point 4 units down and 5 units left: (3-5, 27-4)=(-2, 23)      Consider  [latex]y=(x+5)^{3}-4[/latex] for x=-2     [latex](-2+5)^{3}-4=(3)^{3}-4=27-4=23[/latex]

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