Question

Use the graph of the function y= f(x) below to answer the questions

Answer 1

a. No, f(-3) is not positive.

b. The values of x for which f(x) equals 0 are x = -2, 1, 4.

c. The intervals in which the function f(x) is less than 0 for the values of x are [-3, -1] ∪ [-1, 0).

In Mathematics and Geometry, a function defines and represents the unique relationship that exists between two or more variables in a relation, table, ordered pair, or graph.

Part a.

By critically observing the graph of this function y = f(x), we can logically deduce the following output value;

f(-3) = -5.

Therefore, f(-3) is not positive.

Part b.

The x-intercept of any function is the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y or f(x)" is equal to zero (0);

x-intercepts of f(x): (-2, 0), (1, 0) and (4, 0).

Part c.

By critically observing the graph of this function y = f(x), we can logically deduce that the intervals in which the function f(x) is less than 0 for the values of x lies in both quadrant II and quadrant III;

[-3, -1] ∪ [-1, 0)

Answer 2

a)

We need to find the value of f(-3), that means we need to find the value of the y-coordinate when the x-coordinate is -3

As we can see in the graph

f(-3)=-5

Therefore f(-3) is negative

The answer for this part is NO

b)

if f(x)=0, that means that we are looking for the x-intercepts

x=-2

x=1

x=4

The answer is -2,1,4

c)

We need to know for what values of x f(x)<0

In this case in interval notation

`\lbrack-3,2)\cup(1,4)`