Question

Functions f(x) and g(x) are described as follows: f(x) = −5x2 + 9 x g(x) 0 0 1 4 2 8 3 4 4 0 Which statement best compares the maximum value of the two functions?

Answer 1

Let's look at the description for g(x) first. On the left we have the input (like the horizontal axis on a graph) and on the right is the output, or the value of the function (the vertical axis on a graph). If you look on that right list, the highest number is 8.  This is the maximum value of g(x).  Now we have to compare this to f(x). Looking at f(x), it's an upside-down parabola (like a frown), with starts at 9 on the vertical axis and goes down from there.  You can see this if you think about plugging in x=0.  Then f(0)=9.  If you plug in any other number for x, it gets squared, then multiplied by -5, o you have 9 + [negative number], which will be less than 9. So the maximum value for f(x) is 9. Since 9 is 1 unit larger than 8 (the max for g(x))