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Exercises for Question Type 7: Sketching graphs of polynomials using technology - IB | RevisionDojo

Question 1

The use of a graphing calculator (GDC) is required for this question.

Sketch the graph of $q(x) = x^5 - 5x^3 + 4x$ using technology and approximate all its real roots.

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Question 2

Sketch $u(x)=-x^3+4x$ using graphing technology and determine the intervals on which the function is increasing or decreasing.

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Question 3

Sketch the graph of $h(x)=x^4-4x^2+1$ . Determine its end behavior and find the real roots, correct to two decimal places.

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Question 4

Consider the function $r(x) = 0.5x^4 - x^2 + 2$ .

Using technology, sketch the graph of $r(x)$ .

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Find the coordinates of all turning points.

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State the intervals of concavity.

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Question 5

Sketch the graph of $f(x)=x^3-6x^2+9x+5$ using graphing software. Then determine the coordinates of its turning points.

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Question 6

Graph $w(x)=2x^5-3x^3+x$ using technology. Approximate the coordinates of its turning points and inflection points.

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Question 7

Use technology to graph $t(x)=x^4-x$ and find all values of $x$ such that $t(x)=2$ . Give your answers to two decimal places.

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Question 8

Sketch the graph of $s(x) = x^3 - x$ for $-2 \le x \le 2$ . Use your graph to solve the equation $s(x) = 2$ , giving your answer correct to one decimal place.

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Question 9

Sketch the graph of $g(x) = (x-1)^2(x+2)$ with technology, then list all $x$ -intercepts and classify the nature of each (crossing or touching).

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Question 10

Use graphing software to sketch $v(x)=x^4-2x^2+1$ . Identify its real zeros and state their multiplicities.

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Question 11

Sketch $p(x)=-2x^3+x^2+3x-1$ using technology. Then find all solutions to $p(x)=2$ to two decimal places.

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Question Type 7: Sketching graphs of polynomials using technology Exercises