Question

Suppose that for a function g (x), g (4) = 7. Select all of the statements that are true.
A. 4 is in the range of g.
B. For a value a, it is possible that g (a) = 4.
C. For a value y, it is possible that g (4) = y.
D. The point (4,7) is on the graph of y = g (x).
E. The point (7,4) is on the graph y = g (x).

Answer 1

Answer:

if x=0 then they have same value

1st and 2nd options are out

for x=-1

g(-1)=1

h(-1)=-1

3rd is true

4th

false

for all values except zero, g(x)>h(x)

correct ones are

g(x) > h(x) for x = -1.

For positive values of x, g(x) > h(x).

For negative values of x, g(x) > h(x).

Step-by-step explanation:

Answer 2

Answer:

B and D

Step-by-step explanation:

The wording in the answer choices make a huge difference. It is possible implies that there is a possibility

A is false. The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)

A good example is a constant function such as g(x) = 7. Here, whatever the value of x, the y value is always 7. This represents a horizontal line passing through y = 7. So the range is just a single number {7}

B can be true. It is possible but not a certainty that f(a) = 4 for some value of a. For example, consider the function g(x) = x + 3.

At x = 4, g(4) = 4 .1 + 3 = 7

At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output

C is false. A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.

D is true. Since at x =4, y = g(x) = 7, this corresponds to a point on the graph. The point will be (x=4, y =7) or (4,7)

E is false. The x, y coordinates have been interchanged in this answer choice