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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Go through the statements one at a time.

1. An absolute maximum means that the curve has its highest point at its vertex. That $g(x)$ has a maximum point is then **true**.

2. The statement that $f(x)$ has a vertex is **true**, because there is a point where the functions changes from decreasing to increasing.

3. A negative $x^2$-term gives a sad mouth according to the direction of a quadratic function. Since it's **true** that $g(x)$ has an absolute maximum, it's also **true** that it has a negative $x^2$-term.

4. The function $f(x)$ has an absolute minimum point, and, thus, a minimum value. Then, it continues infinitely far upwards, so it never reach any maximum value. Therefore, the statement is **false**.

5. Because the axis of symmetry goes through the minimum point, and is on the **negative** $x$-axis for $f(x)$ the line of symmetry can not have the positive $x$-value $5.$ So this claim is **false**.