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SAT II Math II : X-intercept and y-intercept

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

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Example Question #12 : Functions And Graphs

What is the x-intercept and y-intercept of:

y=2x-8

Possible Answers:

x-intercept=2

y-intercept=-4

x-intercept = 1

y-intercept = -2

x-intercept= 4

y-intercept= -8

x-intercept=-8

y-intercept=4

Correct answer:

x-intercept= 4

y-intercept= -8

Explanation:

The x-intercept is the value of x that will result in the y value equalling zero and the y-intercept is the y value that results when the x equals zero.

Therefore we replace x with zero to find the y-intecerpt.

y=2(0)-8

y=-8

Now we replace the y with a zero and find our x-intercept

0=2x-8

8=2x

4=x

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Example Question #13 : Functions And Graphs

What is the y-intercept and x-intercept of the function:

y-4=x+8

Possible Answers:

x-intercept=-10

y-intercept=10

x-intercept=-12

y-intercept=12

x-intercept=12

y-intercept=12

x-intercept=-1

y-intercept=2

Correct answer:

x-intercept=-12

y-intercept=12

Explanation:

To find the x and y intercept of the function we need to do algebraic opperations first and then plug in zero for x to find the y-intercept and plug in zero for y to find the x-intercept.

y-4=x+8

y=x+12

y-intercept

y=0+12=12

x-intercept

0=x+12

-12=x

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Example Question #3 : X Intercept And Y Intercept

Define $g(x)=5- \log _{4}\left ( x+5 \right )$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

4.83

4.14

4.60

6.16

3.84

Correct answer:

3.84

Explanation:

Evaluate g(0) :

$g(x)=5- \log _{4}\left ( x+5 \right )$

$g(0)=5- \log _{4}\left ( 0+5 \right )$

$=5- \log _{4} 5$

$=5- \frac{\ln 5}{\ln 4}$

$\approx 5- \frac{1.6094}{1.3863}$

$\approx 5- 1.16$

$\approx 3.84$

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Example Question #1 : X Intercept And Y Intercept

Define $f(x) = 2 \cdot 3^{x-4}- 7$

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

The graph of has no -intercept.

4.18

4.42

6.98

5.14

Correct answer:

5.14

Explanation:

Set f(x) = 0 and solve for :

$f(x) = 2 \cdot 3^{x-4}- 7$

$2 \cdot 3^{x-4}- 7= 0$

$2 \cdot 3^{x-4}=7$

$3^{x-4}=\frac{7}{2} = 3.5$

$\ln \left (3^{x-4} \right )= \ln 3.5$

$(x-4 ) \ln 3 = \ln 3.5$

$x-4 = \frac{\ln 3.5}{ \ln 3} \approx \frac{1.2528}{1.0986} \approx 1.14$

$x\approx 5.14$

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Example Question #5 : X Intercept And Y Intercept

Define $g(x) = 3 + \sqrt[4]{3x-5}$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

1.50

1.68

4.50

The graph of has no -intercept.

4.32

Correct answer:

The graph of has no -intercept.

Explanation:

Evaluate g(0) :

$g(x) = 3 + \sqrt[4]{3x-5}$

$g(0) = 3 + \sqrt[4]{3\cdot 0-5}$

$g(0) = 3 + \sqrt[4]{ -5}$

A negative number does not have a real even-numbered root, so g(0) is not a real number. Therefore, the graph of has no -intercept.

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Example Question #11 : Properties Of Functions And Graphs

Define $f(x) = 4 + \sqrt[5]{2x-9}$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

2.45

5.20

2.80

The graph of has no -intercept.

5.55

Correct answer:

2.45

Explanation:

Evaluate f(0) :

$f(x) = 4 + \sqrt[5]{2x-9}$

$f(0) = 4 + \sqrt[5]{2 \cdot 0 -9}$

$= 4 + \sqrt[5]{ -9}$

$\approx 4 + (-1.55)$

$\approx 2.45$

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Example Question #2 : X Intercept And Y Intercept

Define $h(x) = 12 + \sqrt[3]{3x-7}$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

13.91

10.83

The graph of has no -intercept.

13.17

10.09

Correct answer:

10.09

Explanation:

Evaluate h(0) :

$h(x) = 12 + \sqrt[3]{3x-7}$

$h(0) = 12 + \sqrt[3]{3\cdot 0 -7}$

$= 12 + \sqrt[3]{ -7}$

$\approx 12 +(-1.91)$

$\approx 10.09$

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Example Question #1 : X Intercept And Y Intercept

$h(x)=6- \log _{3}\left ( x-7 \right )$

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

The graph of has no -intercept.

223

736

Correct answer:

736

Explanation:

Set h(x) = 0 and solve for :

$6- \log _{3}\left ( x-7 \right )=0$

$\log _{3}\left ( x-7 \right )=6$

$x-7 = 3^{6}$

x-7=729

x = 736

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Example Question #1 : X Intercept And Y Intercept

Define $h(x) = 4+ \sqrt[3]{3x-7}$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

The graph of has no -intercept.

$-23\frac{2}{3}$

$23\frac{2}{3}$

Correct answer:

Explanation:

Set h(x) = 0 and solve for :

$4+ \sqrt[3]{3x-7} = 0$

$\sqrt[3]{3x-7} = -4$

$\left (\sqrt[3]{3x-7} \right )^{3}= \left (-4 \right )^{3}$

3x-7 = -64

3x= -57

x = -19

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Example Question #10 : X Intercept And Y Intercept

Define $g(x)=5- \log _{4}\left ( x+5 \right )$ .

Give the -coordinate of the -intercept of the graph of .

Possible Answers:

620

1,019

The graph of has no -intercept.

12,495

49,995

Correct answer:

1,019

Explanation:

Set g(x) = 0 and solve for :

$5- \log _{4}\left ( x+5 \right ) = 0$

$\log _{4}\left ( x+5 \right ) = 5$

$x+5 = 4^{5}$

x+5 = 1,024

x=1,019

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SAT II Math II : X-intercept and y-intercept

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #12 : Functions And Graphs

Example Question #13 : Functions And Graphs

Example Question #3 : X Intercept And Y Intercept

Example Question #1 : X Intercept And Y Intercept

Example Question #5 : X Intercept And Y Intercept

Example Question #11 : Properties Of Functions And Graphs

Example Question #2 : X Intercept And Y Intercept

Example Question #1 : X Intercept And Y Intercept

Example Question #1 : X Intercept And Y Intercept

Example Question #10 : X Intercept And Y Intercept

All SAT II Math II Resources

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