use the graph of the function f shown to answer parts (a)-(n).\n(a) find f(-7) and f(-3).\nf(-7)= \nf(-3)=…

use the graph of the function f shown to answer parts (a)-(n).\n(a) find f(-7) and f(-3).\nf(-7)= \nf(-3)= \n(b) find f(6) and f(0).\nf(6)= \nf(0)= \n(c) is f(2) positive or negative?\npositive\nnegative\n(d) is f(-2) positive or negative?\nnegative\npositive\n(e) for what value(s) of x is f(x)=0?\nx= \n(use a comma to separate answers as needed.)\n(f) for what values of x is f(x)>0?\n\n(type a compound inequality. use a comma to separate answers as needed.)\n(g) what is the domain of f?\nthe domain of f is {x| \n(type a compound inequality.)

use the graph of the function f shown to answer parts (a)-(n).\n(a) find f(-7) and f(-3).\nf(-7)= \nf(-3)= \n(b) find f(6) and f(0).\nf(6)= \nf(0)= \n(c) is f(2) positive or negative?\npositive\nnegative\n(d) is f(-2) positive or negative?\nnegative\npositive\n(e) for what value(s) of x is f(x)=0?\nx= \n(use a comma to separate answers as needed.)\n(f) for what values of x is f(x)>0?\n\n(type a compound inequality. use a comma to separate answers as needed.)\n(g) what is the domain of f?\nthe domain of f is {x| \n(type a compound inequality.)

Answer

Explanation:

Step1: Find ( f(-7) ) and ( f(-3) )

For ( f(-7) ), when ( x = -7 ), from the graph, the ( y - )value (since ( y=f(x) )) is ( - 8 ). So ( f(-7)=-8 ). For ( f(-3) ), when ( x=-3 ), from the graph, the ( y - )value is ( 12 ). So ( f(-3)=12 ).

Step2: Find ( f(6) ) and ( f(0) )

For ( f(6) ), when ( x = 6 ), from the graph, the ( y - )value is ( 8 ). So ( f(6)=8 ). For ( f(0) ), when ( x = 0 ), from the graph, the ( y - )value is ( - 4 ). So ( f(0)=-4 ).

Step3: Determine if ( f(2) ) is positive or negative

When ( x = 2 ), from the graph, the ( y - )value ( ( y=f(2) )) is below the ( x - )axis. So ( f(2)) is negative.

Step4: Determine if ( f(-2) ) is positive or negative

When ( x=-2 ), from the graph, the ( y - )value ( ( y = f(-2))) is above the ( x - )axis. So ( f(-2)) is positive.

Step5: Find ( x ) such that ( f(x)=0 )

The graph intersects the ( x - )axis at ( x=-6,x = 1,x = 4 ). So ( x=-6,1,4 ).

Step6: Find ( x ) such that ( f(x)>0 )

The graph is above the ( x - )axis when ( -6\lt x\lt1 ) or ( 4\lt x\lt6 ).

Step7: Find the domain of ( f )

The left - most ( x - )value is ( x=-7 ) and the right - most ( x - )value is ( x = 6 ). So the domain is ( -7\leq x\leq6 ).

Answer:

a. ( f(-7)=-8 ), ( f(-3)=12 ) b. ( f(6)=8 ), ( f(0)=-4 ) c. Negative d. Positive e. ( x=-6,1,4 ) f. ( -6\lt x\lt1,4\lt x\lt6 ) g. ( -7\leq x\leq6 )