Question

1. If a function f(x) is shifted to the left one unit, what function represents the transformation?

Answer 1

The correct answers are:
1) A;
2) A;
4) D 
3 cannot be done because the graph is not shown.

Explanation: 
1) Shifting a graph to the left, we would normally think of subtracting 1 from the function. However, horizontal translations are the opposite; left means adding 1 to x, while right means subtracting 1 from x.

2) A reflection in the x-axis means the y-coordinate will be negated (the opposite sign). This means that g(x)=-f(x)=-(x^2+5=-x^2-5.

4) To perform a vertical stretch of a function, we multiply by the factor; this gives us y=6x.

Answer 2

1. If a function f(x) is shifted To the left one unit, what function represents the transformation?

A. F(x+1)

Shifting a graph to the left, we would normally think of subtracting 1 from the function. However, horizontal translations are the opposite; left means adding 1 to x, while right means subtracting 1 from x.

2. Let g(x) be the reflection of f(x)=x^2+5 in the X-axis. What is a function rule for g(x)?

A. G(x)=-x^2-5



A reflection in the x-axis means the y-coordinate will be negated (the opposite sign). This means that g(x)=-f(x)=-(x^2+5=-x^2-5.

3.what transformations change the graph of F(x) to the graph of g(x)? F(x)=-7x^2 g(x)=-35x^2+5

D. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 5 and translated up 5 units.

The picture is the work.

4. Write an inequality for the following transformation of y=x: a vertical stretch by a factor of 6.

A. Y=6x

If you draw both  lines, you will see that the new one, y = 6x, looks like the original line y = x, was streched up-down. That is because for the same value of x, for the new line, y = 6x, the value of y-coordinated is higher if x is positive or lower if x is negative than for the  original line y =x.