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Which statements about the behavior of f(x) = x2 + 4x − 3 are true? Select all that apply.
A. f has an axis of symmetry at x = –2.
B. The range of f is the set of all real numbers.
C. The maximum value of f is –7 when x = –2.
D. As x approaches infinity, f(x) approaches infinity.
E. As x approaches negative infinity, f(x) approaches negative infinity.

Sagot :

Semsee45idn

Answer:

A, D

Step-by-step explanation:

Given function:  [tex]f(x)=x^2+4x-3[/tex]

Axis of symmetry

[tex]\textsf{Axis of Symmetry formula : }x=-\dfrac{b}{2a}[/tex]

for a quadratic equation in standard form [tex]y=ax^2+bx+c[/tex]

[tex]\implies \textsf{Axis of symmetry}: x=-\dfrac{4}{2}=-2[/tex]

Maximum/Minimum point (vertex)

The max/min point is the turning point of the parabola.

The x-value of the turning point is the axis of symmetry.

[tex]\implies \textsf{Turning point}:f(-2)=(-2)^2+4(-2)-3=-7[/tex]

Turning point (vertex) = (-2, -7)

As the leading coefficient is positive, the parabola opens upwards.  Therefore, the turning point  (-2, -7) will be a minimum.

Domain & Range

Domain: input values → All real numbers

Range: output values → [tex]x\geq -7[/tex]  [as (-2, -7) is the minimum point]

End behavior

As the leading degree is positive and the leading coefficient is positive:

[tex]f(x) \rightarrow + \infty, \textsf{ as } x \rightarrow - \infty[/tex]

[tex]f(x) \rightarrow + \infty, \textsf{ as } x \rightarrow + \infty[/tex]

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