X-intercept and y-intercept - SAT Subject Test in Math II

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Question

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

Answer

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.

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

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Question

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

Answer

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-intercept

x-intercept

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Question

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

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

Answer

Set 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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Question

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

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

Answer

Set and solve for :

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

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

$x-7 = 3^{6}$

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Question

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

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

Answer

Evaluate :

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

$f(0) = 2 \cdot 3^{0-4}- 7$

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

$= 2 \cdot \frac{1}{81}- 7$

$= \frac{2}{81}- 7$

$=-6 \frac{79}{81} \approx -6.98$

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Question

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

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

Answer

Evaluate :

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

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

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

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

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

$\approx 5- 1.16$

$\approx 3.84$

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Question

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

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

Answer

Set and solve for :

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

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

$x+5 = 4^{5}$

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Question

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

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

Answer

Evaluate :

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

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

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

A negative number cannot have a logarithm, so is an undefined expression. Therefore, the graph of has no -intercept.

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Question

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

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

Answer

Evaluate :

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

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

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

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

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Question

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

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

Answer

Evaluate :

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

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

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

$\approx 4 + (-1.55)$

$\approx 2.45$

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Question

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

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

Answer

Evaluate :

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

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

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

$\approx 12 +(-1.91)$

$\approx 10.09$

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Question

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

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

Answer

Set and solve for :

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

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

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

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Question

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

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

Answer

Set and solve for :

$3 + \sqrt[4]{3x-5} = 0$

$\sqrt[4]{3x-5} = -3$

This equation has no solution, since a principal even root of a real number must be positive.

The graph of has no -intercept.

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Question

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

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

Answer

Set and solve for :

$4 + \sqrt[5]{2x-9} = 0$

$\sqrt[5]{2x-9} = -4$

$\left (\sqrt[5]{2x-9} \right ) ^{5}= \left (-4 \right ) ^{5}$

$x=-507\frac{1}{2}$

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Question

Find the intercept of the function.

Answer

The function will cross the x axis when the y coordinate is equal to zero. To find the x intercept plug in the value zero for y and then solve the equation for x. This will be the x coordinate where the function crosses the x-axis, or the x intercept.

$x=\pm \sqrt{2}$

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Question

Find the x-intercept of the following equation:

Answer

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$y=2x+6\rightarrow 0=2x+6$

Subtract 2x from both sides, then divide by -2 to get x by itself:

$\frac{-2x}{-2}=\frac{6}{-2}$

This gives a final answer of x=-3

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Question

Find the x-intercept of the following equation:

Answer

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$2x+y=12\rightarrow 2x+0=12$

Divide by 2 to get x by itself:

$\frac{2x}{2}=\frac{12}{2}$

This gives a final answer of x=6

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Question

Find the x-intercept of the following equation:

Answer

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$y=4x-16\rightarrow 0=4x-16$

Subtract 4x from both sides, then divide by -4 to get x by itself:

$\frac{-4x}{-4}=\frac{-16}{-4}$

This gives a final answer of x=4

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Question

Find the x-intercept of the following equation:

Answer

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$2y+6x=5\rightarrow 0+6x=5$

Divide by 6 to get x by itself:

$\frac{6x}{6}=\frac{5}{6}$

This gives a final answer of x=5/6

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Question

Find the y-intercept of the following equation:

Answer

In order to find the y-intercept, set x=0 then solve for y. For this equation that looks as follows:

$y=6x+2\rightarrow y=0+2$

This gives a final answer of y=2

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