analyzing key aspects of a functions graph\nuse the graphing tool to determine the true statements regarding…

analyzing key aspects of a functions graph\nuse the graphing tool to determine the true statements regarding the represented function. check all that apply.\n$f(x)>0$ over the interval $(1,\\infty)$.\n$f(x)\\leq0$ over the interval $1,\\infty)$.\n$f(x)\\leq0$ over the interval $(-\\infty,1$.\n$f(x)>0$ over the interval $(-\\infty,1)$.\n$f(x)>0$ over the interval $(-\\infty,\\infty)$.

analyzing key aspects of a functions graph\nuse the graphing tool to determine the true statements regarding the represented function. check all that apply.\n$f(x)>0$ over the interval $(1,\\infty)$.\n$f(x)\\leq0$ over the interval $1,\\infty)$.\n$f(x)\\leq0$ over the interval $(-\\infty,1$.\n$f(x)>0$ over the interval $(-\\infty,1)$.\n$f(x)>0$ over the interval $(-\\infty,\\infty)$.

Answer

Explanation:

Step1: Analyze the function's graph for (x>1)

Observe that for (x\in(1,\infty)), the graph of (y = f(x)) is above the (x -)axis, so (f(x)>0) for (x\in(1,\infty)).

Step2: Analyze the function's graph for (x\geq1)

Since (f(x)>0) for (x\in(1,\infty)), the statement (f(x)\leq0) for (x\in[1,\infty)) is false.

Step3: Analyze the function's graph for (x\leq1)

The graph is below the (x -)axis for some values of (x\in(-\infty,1]), but also above for some values. So (f(x)\leq0) for (x\in(-\infty,1]) is false.

Step4: Analyze the function's graph for (x < 1)

The graph is below the (x -)axis for some (x\in(-\infty,1)), so (f(x)>0) for (x\in(-\infty,1)) is false.

Step5: Analyze the function's graph for all real - numbers

The graph is below the (x -)axis for some values of (x), so (f(x)>0) for (x\in(-\infty,\infty)) is false.

Answer:

(f(x)>0) over the interval ((1,\infty))