Intercepts of Functions

What is the method for finding x-intercepts of linear functions?

• Setting y = 0 and solving for x

• Setting x = 0 and solving for y

• Taking the derivative of the function

• Multiplying the function by 2

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CCSS.HSA.REI.B.3

CCSS.HSA.REI.D.11

How do you find the y-intercepts of quadratic functions?

• Set y=0 and solve for x

• Set x=0 and solve for y

• Count the number of x-intercepts

• Use the Pythagorean theorem

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CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

What is the process for identifying x-intercepts of exponential functions?

• Multiply the function by 2

• Set the function equal to zero and solve for x.

• Take the derivative of the function

• Divide the function by x

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CCSS.HSA.CED.A.1

CCSS.HSA.REI.D.11

What is the significance of x-intercepts in the context of functions?

• They indicate the maximum value of the function

• They indicate the values of x for which the function equals zero.

• They represent the y-values of the function

• They show the slope of the function at that point

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CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11

Explain the relationship between x-intercepts and roots of a function.

• The x-intercepts of a function are only found in quadratic equations, while the roots can be found in any type of function.

• The x-intercepts of a function are unrelated to the roots of the function.

• The x-intercepts of a function are the same as the roots of the function.

• The x-intercepts of a function are always negative, while the roots can be positive or negative.

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CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11

What are the different scenarios in which a quadratic function may not have real x-intercepts?

• The parabola is a perfect square trinomial and does not intersect the x-axis.

• The parabola opens downward and does not intersect the x-axis.

• The parabola intersects the x-axis at imaginary points.

• The parabola opens upward and does not intersect the x-axis.

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CCSS.HSA.APR.B.3

How can you determine the y-intercept of a function from its equation?

• Multiply the function by 2.

• Set x=0 and solve for y.

• Take the derivative of the function.

• Set y=0 and solve for x.

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CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Discuss the graphical representation of x-intercepts and y-intercepts of a function.

• Locate the points where the graph intersects the x-axis and y-axis

• Measure the distance between the x-intercept and y-intercept

• Find the slope of the graph at the x-intercept and y-intercept

• Count the number of lines intersecting the x-axis and y-axis

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CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSF.IF.B.4

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Explain the concept of intercepts in the context of functions and their applications in real-life scenarios.

• Intercepts are the points where a function reaches its maximum value (max-intercept) or minimum value (min-intercept).

• In real-life scenarios, intercepts have no practical applications and are purely theoretical concepts.

• Intercepts are the points where a function crosses the z-axis (z-intercept) or the w-axis (w-intercept).

• Intercepts are the points where a function crosses the x-axis (x-intercept) or the y-axis (y-intercept). In real-life scenarios, intercepts can represent important values such as the break-even point in business or the time and distance at which two objects intersect in physics.

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CCSS.HSF.IF.B.4

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What are the similarities and differences between x-intercepts and y-intercepts of functions?

• x-intercepts occur when the graph is increasing and y-intercepts occur when the graph is decreasing

• x-intercepts occur when y=0 and y-intercepts occur when x=0

• x-intercepts occur when x=0 and y-intercepts occur when y=0

• Both intercepts are points where the graph crosses an axis, but x-intercepts occur when y=0 and y-intercepts occur when x=0.

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CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7