0. Functions

Common Functions

0. Functions

Common Functions

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Multiple Choice

Identify the ordered pair of the vertex of the parabola. State whether it is a minimum or maximum.

$\left(-3,-2\right);$ maximum

$\left(-3,-2\right);$ minimum

$\left(-1,2\right);$ maximum

$\left(-1,2\right);$ minimum

Verified step by step guidance

Observe the graph of the parabola. It opens upwards, indicating that the vertex is a minimum point.

Identify the vertex of the parabola on the graph. The vertex is the lowest point on the graph.

Locate the coordinates of the vertex. From the graph, the vertex is at the point (-3, -2).

Since the parabola opens upwards, the vertex represents a minimum value of the function.

Conclude that the ordered pair of the vertex is (-3, -2) and it is a minimum.

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Textbook Question

In Exercises 67–72, you will explore some functions and their inverses together with their derivatives and tangent line approximations at specified points. Perform the following steps using your CAS:

b. Solve the equation y=f(x) for x as a function of y, and name the resulting inverse function g.

67. y= √(3x-2), 2/3 ≤ x ≤ 4, x_0=3

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Textbook Question

b. Solve the equation y=f(x) for x as a function of y, and name the resulting inverse function g.

68. y= (3x+2)/(2x-11), -2 ≤ x ≤ 2, x_0=1/2

Textbook Question

b. Solve the equation y=f(x) for x as a function of y, and name the resulting inverse function g.

72. y= 2-x-x³, -2 ≤ x ≤ 2, x_0 = 3/2

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Multiple Choice

In the graph shown, identify the y–intercept & slope. Write the equation of this line in Slope-Intercept form.

Where is the axis of symmetry located on the given parabola?

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=4x^3+\frac12x^{-1}-2x+1$

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=2+x$

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=3x^2+5x+2$

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