Question

Question 7 of 10

Answer 1

The leading coefficient determines the shape of the graphs, such as how

the characteristic of a function are directed.

Correct response:

The graphs that represents functions that have a negative leading

coefficient are;

• Graph A, Graph B, and Graph C

Methods by which the correct options are selected

Graph A:

The function in graph A is x³

When the coefficient of x³ is negative, the value of the function rises as x decreases from 0 to -∞, and decreases as x increases from 0 to ∞

Therefore;

• The leading coefficient of Graph A is negative.

Graph B:

The value of the graph decreases as the magnitude of x increases

therefore, the graph is similar to a quadratic function, such that the leading

coefficient is negative, which inverts the function to give increasing output

with negative value as the value of x increases.

Therefore;

• The leading coefficient of the quadratic function in Graph B is negative.

Graph C:

The given function in graph C is a linear function having a negative slope,

therefore;

• The leading coefficient of x in the function in Graph C is negative.

Graph D:

The function of the graph in Graph D, that have y values that increases

exponentially as x increases is a quadratic function.

Given that y increases as the value of x increases, the leading coefficient

(coefficient of x²) is positive.

Therefore;

• The graphs that represents functions that have negative leading coefficient are; Graph A, Graph B, and Graph C.

Learn more about the factors that depend on leading coefficient of a function here:

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