Answer:
The correct option is 4.
Step-by-step explanation:
The given function is
[tex]h(x)=-2^x+8[/tex]
The graph of another function g(x) is shown in give figure.
Choose any point from the given intervals and check whether the function g(x) is greater than h(x) or not.
For interval [tex]-2\leq x\leq -1[/tex].
Put x=-2 in the given function h(x).
[tex]h(x)=-2^(-2)+8[/tex]
[tex]h(x)=-0.25+8=7.75[/tex]
The value of h(x) at x=-2 is 7.75.
From the given graph it is noticed that the value of g(x) at x=-2 is 1.
Since g(x)<h(x) at x=-2, therefore option 1 is incorrect.
For interval [tex]-1\leq x\leq -0[/tex] and [tex]0\leq x\leq 1[/tex]
Put x=0 in the given function h(x).
[tex]h(x)=-2^(0)+8[/tex]
[tex]h(x)=-1+8=7[/tex]
The value of h(x) at x=0 is 7.
From the given graph it is noticed that the y-intercept of g(x) is 3.
Since g(x)<h(x) at x=0, therefore option 2 and option 3 are incorrect.
For interval [tex]1\leq x\leq 2[/tex].
Put x=2 in the given function h(x).
[tex]h(x)=-2^(2)+8[/tex]
[tex]h(x)=-4+8=4[/tex]
The value of h(x) at x=2 is 4.
From the given graph it is noticed that the value of g(x) at x=2 is more than 10.
Since g(x)>h(x) at x=2, therefore option 4 is correct.
