use the graphing tool to determine the true statements regarding the represented function. check all that…

use 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) ).

use 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 graph for (x\in(1,\infty))

Observe the graph for (x > 1). The function values are above the (x -)axis, so (f(x)>0) for (x\in(1,\infty)).

Step2: Analyze the graph for (x\in[1,\infty))

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

Step3: Analyze the graph for (x\in(-\infty,1])

The function has positive and negative values for (x\in(-\infty,1]), so the statement (f(x)\leq0) for (x\in(-\infty,1]) is false.

Step4: Analyze the graph for (x\in(-\infty,1))

The function has positive and negative values for (x\in(-\infty,1)), so the statement (f(x)>0) for (x\in(-\infty,1)) is false.

Step5: Analyze the graph for (x\in(-\infty,\infty))

The function has negative - valued parts, so the statement (f(x)>0) for (x\in(-\infty,\infty)) is false.

Answer:

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