Which transformations have been performed on the graph of f(x) = to obtain the graph g(x) = 1/4 + 6 select each correct answer. (a) reflect the graph over the x-axis (b) compress the graph closer to the x-axis (c) translate the graph down (d) translate the graph to the right (e) translate the graph to the left (f) translate the graph up (g) stretch the graph away from the x-axis

The correct answers are B, E and F

Step-by-step explanation:

We can find the answer B by noticing the 1/4 put in front of the cube root sign. this 1/4 shirks the value of every y value by 1/4, which in turn makes it closer to the x axis.

We can find answer E by looking at the 3 inside of the cube root symbol. When we add a number underneath the cube root sign, it always moves the value to the left that many spaces.

Finally, we can find F by looking at the 6 at the end. Any number added to the end of an equation as a constant moves the graph up by that many spaces.

You can break down the image into the triangle and semicircle, find the area of each, and add the areas together to get the total area of the figure.

1) Area of triangle
The equation for the area of a triangle is: 
where A = area, b = length of base, and h = height of triangle.

Looking at the attached picture, the base (green line), b = 8, and the height (blue dashed line), h = 4. Plug these values into .


2) Area of semicircle
The equation of the area of a semicircle is simply the area of the circle divided by 2, making the equation: 
where A = area and r = radius of the circle.

The radius of the circle is half of the diameter (green line in picture). That means the radius, r = 8/2 = 4. Plug that into the equation and solve for area of the semicircle:


3) Add the areas of the triangle and semicircle together


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