The graph of g is a vertical translation of the graph of the parent linear function. A right triangle with an area of 8 square units is f...

Question

The graph of g is a vertical translation of the graph of the parent linear function. A right triangle with an area of 8 square units is formed by the x-axis, the y-axis, and the graph of g. Write an equation for g.

Answer 1

The parent linear function is f(x) = x. This graph has a slope of 1 and intercept (0, 0). A vertical translation means it is shifted up or down. Notice that if this graph is shifted up or down, it forms a right triangle with the x and y axis as two sides of the triangle. The area of a right triangle is (base x height)/2. In this case, the base is on the x-axis and the height is the distance on the y-axis. Since the slope of this line is 1, we know that the base and height must be the same (change in y equals change in x).

So (base x height)/2 = 8, which means (base x height) = 16. So the base and height must equal 4. So the graph is shifted 4 units up or 4 units down. From the information given, it could be either up or down, so there are two possible answers. The equation could be g(x) = x + 4 or g(x) = x - 4.