Answer
a. $(-\infty,\infty)$
b. $\emptyset$
c. see explanations.
Work Step by Step
a. As the graph is entirely above the x-axis, the solution set for $y\gt0$ is all real numbers or $(-\infty,\infty)$
b. Again, as the graph is entirely above the x-axis, the solution set for $y\lt0$ is an empty set or $\emptyset$
c. With $y=4x^2-8x+7$, we have $y=4(x^2-2x+1)+3=4(x-1)^2+3$. As the term $(x-1)^2\geq0$, we have $y\gt0$ for all real numbers, and $y\lt0$ gives an empty set.
