SAT Mathematics Practice Test 5

If $\mathit{f}$ is a function of $\mathit{x}$, then the graph of f in the xy-plane consists of all points $\left(\mathit{x},\mathit{f}\left(\mathit{x}\right)\right)$. An $\mathit{x}-$ intercept is where the graph intersects the $\mathit{x}-$axis; since all points on the $\mathit{x}-$axis have $\mathit{y}-$ coordinate 0, the graph of f will cross the x-axis at values of $\mathit{x}$ such that $\mathit{f}\left(\mathit{x}\right)=0.$ Therefore, the graph of a function $\mathit{f}$ will have no $\mathit{x}-$intercepts if and only if f has no real zeros Likewise, the graph of a quadratic function with no real zeros will have no x-intercepts.
Choice A is incorrect. The graph of a linear function in the xy-plane whose rate of change is not zero is a line with a nonzero slope. The x-axis is a horizontal line and thus has slope 0, so the graph of the linear function whose rate of change is not zero is a line that is not parallel to the $\mathit{x}-$axis. Thus, the graph must intersect the x-axis at some point, and this point is an x-intercept of the graph. Choices B and D are incorrect because the graph of any function with a real zeromust have an x-intercept.